blackpenredpen series


Change), You are commenting using your Twitter account. If possible, evaluate \( 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + \cdots \), \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{3^n n! Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n+\sqrt{n}} } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \left[ \frac{1-2n}{3+4n} \right]^n } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{3^n}{2^n+n^2} } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^3}{2n^5+3n-4} } }\) converges or diverges. #tomrocksmaths #shinisomara #uniq. Hes made a number of videos about admissions (playlist here) and if youre thinking about applying then definitely watch his videos. Log in to rate this practice problem and to see it's current rating. I have watched a lot of maths videos on the internet. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^{10}4^n}{n!} battling math Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(-1)^n}{3n+1} } }\) converges or diverges. If possible, evaluate \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n}{2^n} } }\). If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) diverges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ 1/a_n } }\) must converge. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ n \sqrt{\sin(1/n^2)} } }\) converges or diverges. If it is true, prove it. If possible, evaluate \( 1/2 - 1/3 + 2/9 - 4/27 + \cdots \). \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) If possible, evaluate \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(-1)^n}{n!} Ar\UOt\nN~`YV B)1E+j1heVC5m\rbk jgTm}xWHp\K] n(fQl[CiK l#H],-adYE]q!??nzI \aQo;N\3w4pu)Wt[r'kyN61CKdrv=?sv_F}NwrW-MOoG^3pJW]^-Tj0m2 (LogOut/ } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ \cos^2(1/n) } }\). It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. \(\displaystyle{ \sum_{n=1}^{\infty}{ \sqrt[n]{2} - 1 } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^2}{2^n+3^n} } }\). Is this true or false? Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(2n)! \(\displaystyle{ \sum_{n=1}^{\infty}{ \left[ \frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n+1}} \right] } }\). Highlights of the channel include the time he livestreamed solving integrals for six hours straight, his videos about Oxbridge interview questions (which include a collaboration with Tom Rocks maths), and his recent conversation with Po Shen Loh. \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) Determine whether the series \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{2}{\sqrt{n}\ln n} } }\) converges or diverges.

$yL[VOA:4NcZ)D]"lG{)Dh>H Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n-1}{\sqrt{n^3+2n+5}} } }\) converges or diverges. } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ (\pi/2 - \tan^{-1} n) } }\). Make sure to specify the test(s) and theorem(s) you used as part of your final answer. For Divergence (TFD) Geometric Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n\sqrt{n}} } }\) converges or diverges. Similar style to 3Blue1Brown with focus on computer-science related maths, Up And Atom https://www.youtube.com/c/UpandAtom (LogOut/ Great for folks looking to find new techniques. \(\displaystyle{ \sum_{n=1}^{\infty}{ 1 } }\). If possible, determine the value to which the series converges and whether the series converges conditionally or absolutely. Andrew Dotson is a bit like the physics equivalent of Flammable Maths. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt{n!}} \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) If it is false, provide a counter-example. My favourites are New Math, Thats Mathematics, and my girlfriend and I are obsessed with Lobachevsky. Is this true or false? \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\ln(e^n-1)} } }\). Another more physics-related channel, but has existed a long time with weekly uploads and has a lot of good videos, that also talks about the maths of physics. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{2^n n!}{(n+2)!} Series Steve from blackpenredpen answers a real Oxford University maths admissions interview question set by Oxford Mathematician (and interviewing tutor) Dr Tom Crawford. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n! Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n^{1+1/n}} } }\) converges or diverges. So think carefully about what you need and purchase only what you think will help you. Change), You are commenting using your Twitter account. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{\cos(\pi n)}{\ln n} } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^2+1}{n^3+1} } }\) converges or diverges. Practice problem 157 on the Direct Comparison Test page shows the details on proving that \( 1/\ln(n) \geq 1/n \). I have to say, I respect how much detail he goes into, especially in the Banach-Tarski video. He has recurring series on deep learning, differential equations, linear algebra and calculus, all of which are excellent high-level overviews of the respective topics. If possible, evaluate \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) where \( a_1 = 9 \) and \( a_n = (6-n)a_{n-1} \) for \( n \geq 2 \). \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) For what values of \(x\) will the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(x-1)^n}{n \cdot 3^n} } }\) converge? Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt[3]{2^n+1}} } }\) converges or diverges. Some random ones I liked: the 25 horses problem and some deceptively simple geometry problems. # \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{\cos(\pi n)}{\ln n} } }\). K[s >> stream Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{e^{\sqrt{n}}} } }\) converges or diverges. } }\).

pC>EAE9*{"+{~tOO6RG-^hwx H_eC>{pH_ series tan power expansion Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n}{2^n} } }\) converges or diverges. As an Amazon Associate I earn from qualifying purchases. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{3^n n^2}{n!} Simon Clark studied physics at Oxford and is the messiah for physics A-level students applying to Oxbridge. Recommended Books on Amazon (affiliate links), Complete 17Calculus Recommended Books List. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n^{1+1/n^2}} } }\) converges or diverges. For what values of \(x\) will the series \( x^1 + x^2 + x^3 + x^4 + \cdots + x^n + \cdots \) converge? \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{3^{\ln n}} } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(-1)^n}{\tan^{-1}n} } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^3-2n-1}{2n^5+3n-4} } }\). But if you need to brush up on something needed for one of the other channels, I recommend him. If it is true, prove it. \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. \(\displaystyle{ \sum_{n=1}^{\infty}{ \left[ \frac{1}{\sqrt{n}}- \frac{1}{n} \right] } }\). Finishing the problem, we have \( 9 + 36 + 108 + 216 + 216 = 585 \), \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(n! Thanks to Sydney for reading a draft of this post. He also has a second channel, the highlight of which is the time he ran untested viewer-submitted code on his Christmas tree. Is this true or false? Determine whether the series \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{1}{\ln(n)} } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{\sin(2n)}{n+3^n} } }\). Is this true or false? 5 videos on John Conways Game of Life: https://www.youtube.com/playlist?list=PLvA_gXIhzZNXdAyEGJaSA2X15-ibaXh7P This one is of intermediate production value between the guy-with-whiteboard channels and the 3B1B cinematic masterpieces. Is this true or false? The first video below is the video clip that solves this problem. 3Blue1Brown (real name Grant Sanderson) is my favourite maths YouTuber. \( \newcommand{\vhat}[1]{\,\hat{#1}} \) During that solution, he mentions a video about the limit \(\displaystyle{ \lim_{ heta o 0}{ rac{\sin(\theta)}{\theta} } }\). Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{3^n n! \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(n!)^2}{(2n)!} \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(2n+1)^n}{n^{2n}} } }\). Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ (1 - \sin(1/n)) } }\) converges or diverges. [About], \( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) How to speed up an ECLIPSE run: ECLIPSE Convergence Version 2 December 2009 Do NOT follow this link or you will be banned from the site. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n \sin^2 n}{n^3 + 2} } }\) converges or diverges. \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) DC-I Semester-II Lesson: Tests for the Convergence of Infinite Series Cour, rev. DISTILLATION COLUMNS IN CHEMCAD METHOD TO CONVERGE RELUCTANT COLUMNS IN CHEMCAD COLUMN MODELS IN CHEMCAD Th, 005-012 084415 Editorial (D) I enjoy his videos about geometry. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^3-2n-1}{2n^5+3n-4} } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{\sin(2n)}{n+3^n} } }\) converges or diverges. If it converges, find the sum, if possible. There are a number of channels that are good for formal education, like Khan Academy or Organic Chemistry Tutor. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sin^4 n} } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n! ;-|`v2w} %6$Ag^d]m*o/=ax'WE oYtNw vrW-R1W ]V-R]/6xWelVZA44 PoE T:C[23R5V'>)=XZW)6\OGk*/451O|23&maKx. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(2n)! For what values of \(x\) will the series \(\displaystyle{ \sum_{n=0}^{\infty}{ \left[ \sum_{m=0}^{\infty}{ x^m } \right]^n } }\) converge? If \(\displaystyle{ \sum_{n=1}^{\infty}{ (a_n)^2 } }\) converges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) must also converge. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ 0 } }\) converges or diverges. If it is true, prove it. If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) converges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ 1/a_n } }\) must diverge. To keep this site free, please consider supporting me. [Privacy Policy] )^n}{n^{10n}} } }\) converges or diverges. 050107 \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{1}{\ln(n)} } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{\tan(1/n)}{n^2} } }\). e#6NNF10hso4~%X$+aML|3dtdmsP72S}u\wr~m?,^psWp*$A`SV#t!M6(p{`q$wj;@GpX$- Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \sqrt[n]{2} - 1 } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{1}{n\sqrt{n^5-1}} } }\) converges or diverges. Change), You are commenting using your Facebook account. If it is false, provide a counter-example. \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) (LogOut/ \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n(n+2)}{(2n+1)^2} } }\). (LogOut/

If it is false, provide a counter-example. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(-1)^n}{3n+1} } }\). %PDF-1.4 \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{2}{\sqrt{n}\ln n} } }\). He also covers some topics you may not know about, like how the RSA encryption algorithm works. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n} } }\). Explain. 3 0 obj << Address: Copyright 2022 PDFCOFFEE.COM. Mathologer is strongest in animating proofs. Is this true or false? Determine whether the series \(\displaystyle{ \sum_{n=1619}^{\infty}{ \frac{1}{(\ln n)^{\ln n}} } }\) converges or diverges.

If it is false, provide a counter-example. Make sure you support the guy that did this video. Links and banners on this page are affiliate links. Change), You are commenting using your Facebook account. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^n}{3^{n^2}} } }\). If it converges, find the sum, if possible. The videos of his where he does actual maths include finding the eigenvalues of a Mbius strip, integrating with Feynmans technique and the you laugh you differentiate challenge. If it is true, prove it. n |r| 1 Sum = n=1 Telescoping X bn bn+1 n=1 L has to be finite D.N.E.

} }\) converges or diverges. A lot of his videos are vlogs, for people who want to see what life is like as a physics graduate student (hint: its shit). [Support] }{n^n} } }\) converges or diverges. His best videos are: his stand-up routine about spreadsheets, his videos about the hilarious superpermutation saga, and his investigation into whether land area assumes a country is perfectly flat. Hes particularly strong in algebra and calculus. \(\displaystyle{ \sum_{n=1}^{\infty}{ \sin^2(1/n) } }\). Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^{10}4^n}{n!} Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n! Is this true or false? Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ n \sin(1/n) } }\) converges or diverges. The videos of his I like the most are the ones where he talks about his favourite books (click here for the playlist). \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n! \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt{n!}} My favourite videos of his are the ones about error-correcting codes, Dirichlets theorem and his interactive quaternion explainer. This guy hasnt made a video in over two years, but he comes recommended by 3B1B himself, and I recommend his series on self-driving cars, how science works, and a visual introduction to complex numbers. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^n}{(n! or inf Write out several terms and cancel a lot to find partial sum p>1 p1 - lim bn+1 = L X Integral X Limit Comparison (LCT) X an n=1 0 lim n an X n=1 an > 0 Alternating (AST) Ratio (1)n1 bn bn bn+1 bn bn 0 X an+1 =L 0, and bn n=1 X 1 Converges an |an | converges, then X p n |an | = L < 1 X n=1 X an n=1 lim n X |an | diverges, then Try to use p-series or geometric series to compare a known divergent an = L > 0, and bn bn n=1 is known to be divergent This version of LCT is inconclusive if L = 0 or L = Use TFD limn (1)n1 bn 6= 0 (1)n1 = cos (n 1) an+1 =L>1 lim n a Inconclusive if L = 1 Great for ! Is this true or false? Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \ln[ n/(n+2) ] } }\) converges or diverges. If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) converges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ 1/a_n } }\) must diverge. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(-1)^n}{\sqrt{n+1}} } }\) converges or diverges. PBS Space Time https://www.youtube.com/c/pbsspacetime TED-Ed has a puzzle series which includes videos on the prisoner hat riddle, the Mondrian squares riddle, and a variation upon the blue-eyed islander problem. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{2^n}{3^n+n^3} } }\). Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt{n}e^{\sqrt{n}}} } }\) converges or diverges. Like many of these channels, Penn has videos where he works through Olympiad problems and problems from other famous exams like the Putnam. He talks about mostly physics topics, but doesnt gloss over the important mathematical details like is so common. Sort of a mix of physics and computer science related mathematical topics, with cute animations. \(\displaystyle{ \sum_{n=1}^{\infty}{ n \sqrt{\sin(1/n^2)} } }\). All of his videos have the same basic format of working through some problem, animated with Powerpoint. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(-1)^n}{\tan^{-1}n} } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\ln(e^n-1)} } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n^{1+1/n^2}} } }\). Another excellent channel. Learn how we and our ad partner Google, collect and use data. \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \), We use cookies to ensure that we give you the best experience on our website. If it converges, find the sum, if possible. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n^3+3n^2+2n} } }\) converges or diverges. His Christmas specials are good: these two videos featured many other well-known maths personalities, and he goes through problems every day during Papa Flammys advent calendar. x^n } }\) converge? Calculus Series Convergence Tests Original Design: blackpenredpen 2019 Test \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{e^n+1} } }\). The question looks at the divergence of the sum of the reciprocals of the prime numbers, using the Fundamental Theorem of Arithmetic, the divergence of the Harmonic Series (1/n), and the Basel Problem (sum of 1/n2 equals pi-squared over 6). @GXBq6t,_"[ ? Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \sin^2(1/n) } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ (1-1/n)^n } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{3^{\ln n}} } }\). If it is true, prove it. A sneak peek of my upcoming collab with @duolingo - full video coming August 26 at DuoCon. Now she makes videos about what famous mathematicians and physicists were reading or writing, and occasionally shell make a video of her solving a problem herself. If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) and \(\displaystyle{ \sum_{n=1}^{\infty}{ b_n } }\) both converge, then \(\displaystyle{ \sum_{n=1}^{\infty}{ (a_n b_n) } }\) must also converge. However, we do not guarantee 100% accuracy. Pi Day (March 14th) used to inspire a lot more enthusiasm, but I guess its sufficiently mainstream now that its no longer cool? If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) and \(\displaystyle{ \sum_{n=1}^{\infty}{ b_n } }\) both converge, then \(\displaystyle{ \sum_{n=1}^{\infty}{ (a_n + b_n) } }\) must also converge. \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt[3]{2^n+1}} } }\). If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) and \(\displaystyle{ \sum_{n=1}^{\infty}{ b_n } }\) both diverge and \( a_n \neq b_n \), then \(\displaystyle{ \sum_{n=1}^{\infty}{ (a_n - b_n) } }\) must also diverge. All rights reserved. }{e^{n^2}} } }\) converges or diverges. I recommend his conversations with Janna Levin, John Urschel, Frank Wilczek, and Moon Duchin.

Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^2 2^{n+2}}{4^n} } }\) converges or diverges. Vsauce is perhaps the most popular educational YouTuber, and he has touched on maths a number of times.

Watching Veritasium videos was a not insignificant part of what first got 13-year-old me into science. This is part 2 of the interview you can find part 1 on Gabriels Horn here. If possible, evaluate \( 1/2 + 1/6 + 1/12 + 1/20 + \cdots \). Evaluate \(\displaystyle{ \sum_{n=1}^{\infty}{ 0 } }\). \(\displaystyle{ \sum_{n=3}^{\infty}{ \frac{\ln n}{n^2} } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ n \sin(1/n) } }\). 6 videos on Mathematical Games (The Mathematics of Sprouts is particularly interesting) : https://www.youtube.com/playlist?list=PLvA_gXIhzZNV8NzeDJFworZ83KZLtZfzE. If \(\displaystyle{ \sum_{n=1}^{\infty}{ (a_n)^2 } }\) converges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) must also converge. If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) and \(\displaystyle{ \sum_{n=1}^{\infty}{ b_n } }\) both diverge and \( a_n \neq b_n \), then \(\displaystyle{ \sum_{n=1}^{\infty}{ (a_n - b_n) } }\) must also diverge. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sin^4 n} } }\). If it converges, find the sum, if possible. Hopefully you'll find something of use in there - listen at tomrocksmaths.com (link on profile) #tomrocksmaths #expandablemind #podcast, Teaching maths on a football pitch. Their requirements come first, so make sure your notation and work follow their specifications. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ (1-1/n)^{n^2} } }\) converges or diverges. \(\displaystyle{ \sum_{n=1}^{\infty}{ (1-1/n)^n } }\). } }\) converges or diverges. So go to YouTube and like this video and follow him. } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^3}{2n^5+3n-4} } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ \sin(1/n^2) } }\). I Is this true or false? Aleph0 had put out some great content in the past few years: https://www.youtube.com/channel/UCzBjutX2PmitNF4avysL-vg, Here are some enjoyable Recreational Math Videos fro MisterCorzi: }{n^n} } }\). While the production value is significantly lower, he makes up for it with sheer quantity. } }\) converges or diverges. Is this true or false? If it is false, provide a counter-example. Explain. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt{n}e^{\sqrt{n}}} } }\). Determine whether the series \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{1}{\ln(n^n)} } }\) converges or diverges. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^n}{3^{n^2}} } }\) converges or diverges. For what values of \(x\) will the series \( 1^x + 2^x + 3^x + 4^x + \cdots + n^x + \cdots \) converge? For what values of \(x\) will the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{x^n}{n} } }\) converge? If it is true, prove it. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{3^n n^2}{n!} Explain. Science Asylum https://www.youtube.com/c/Scienceasylum Is this true or false? In short, use this site wisely by questioning and verifying everything. Explain. 5 Videos on the Penrose Tiles (No 5 stands alone): https://www.youtube.com/playlist?list=PLvA_gXIhzZNU3KF3yE9YTcJvV_k7810wC A really great youtube channel, one of my favourites in fact. \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{e^{\sqrt{n}}} } }\). /Length 3782 Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt{n} - \sqrt{n+1}} } }\) converges or diverges. This is the most well-known maths channel. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^2}{2^n+3^n} } }\) converges or diverges. If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) converges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n / n } }\) must also converge. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \sin(1/n^2) } }\) converges or diverges. THE CONVERGENCE-CONFINEMENT METHOD AFTES welcomes comments on this paper What you may not know, however, is that Tom Lehrer had an entire career as a mathematical musician! Is this true or false? Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n+3^n} } }\) converges or diverges. Since its very difficult to communicate mathematics purely orally, maths podcasts are really more about the characters involved and their personal stories. I am especially pleased by his Simpsons-themed videos. I particularly enjoyed their exploration of voting systems and the Condorcet paradox (which I wrote about in my Beginning of Infinity review). By using this site, you agree to our, Solve Linear Systems with Inverse Matrices, Piecewise Functions - The Mystery Revealed. When using the material on this site, check with your instructor to see what they require. Do you have a practice problem number but do not know on which page it is found? We carefully choose only the affiliates that we think will help you learn. He has a great video addressing the infamous Numberphile claim that the sum of all natural numbers is -1/12. Did you know that only 6% of Korean 11-year-olds could solve this problem?! \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{\sqrt{n} - \sqrt{n+1}} } }\). For what values of \(x\) will the series \(\displaystyle{ \sum_{n=0}^{\infty}{ \left[ \frac{1}{1-x} \right]^n } }\) converge? Even if you didnt understand anything he was talking about, 3B1Bs videos are still worth watching for the pure art and enthusiasm. Log in to rate this page and to see it's current rating. I enjoy Shefs of Problem Solving a great deal https://www.youtube.com/channel/UCGnDWH8_ClXegQkWnbzDnzA. \(\displaystyle{ \sum_{n=2}^{\infty}{ \frac{1}{n\sqrt{n^5-1}} } }\). (LogOut/ For what values of \(k\) will the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{x(\ln x)^k} } }\) converge? \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{3^n}{2^n+n^2} } }\). \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) He also has a meme-y aesthetic and sense of humour that can become a bit much at times. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \left[ \frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n+1}} \right] } }\) converges or diverges. We just think his videos will help you.). DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. Mathmaniac also has a series about group theory, inspired by 3B1Bs series about calculus and linear algebra. I love chemical formulae and this is one of my favourites. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{(n! We talked about our experiences of studying for a PhD and how our careers have developed as a result. Finally, here is this posts obligatory link to a quantum computing video. [emailprotected] If possible, evaluate \(\displaystyle{ \sum_{n=1}^{\infty}{ (e^{1/n} - e^{1/(n+2)}) } }\). \(\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n^n}{(n! TheGermanFox has only uploaded three videos, but his musical proof of why e is irrational is actually really good and I cant get it out of my head. To bookmark this page and practice problems, log in to your account or set up a free account. If it is true, prove it. Determine whether the series \(\displaystyle{ \sum_{n=1}^{\infty}{ e^{-n}\sin(n) } }\) converges or diverges. Unless otherwise instructed, determine the convergence or divergence of these series. If \(\displaystyle{ \sum_{n=1}^{\infty}{ a_n } }\) diverges, then \(\displaystyle{ \sum_{n=1}^{\infty}{ 1/a_n } }\) must converge. This podcast, hosted by Grant Sanderson, has just started recently, but I can already recommend the conversations with Steven Strogatz and Sal Khan (of Khan Academy fame). U2PLjF?7YR41i48FCb$)_|``bF4b=QN P=!>ZoEZMZbhwt2nSh2^!n&H)!T?_M#jH1L~.`L|B"J BE!b! x\Ys~X}TlWQq%6Jj9C#`0`wi(Uhuo~{"g#~F@Ra)fw?^p\7s}fajPmw?ow]]o~wWd1$g1dl?}{3z3[_ OrN2"O-(JI8b@FH7eH0ABYDrZbx#s4f.-{ a%v5*(2XzD5Dw7}TFokC&QZb'sDjFb "EM 6w+bCvR|i K!6P@`];GAx&A&8qCb}'NAn ' A7UF(!9{Vv=F>c^N(l{EJTJ;\B0\]%`r7fwRC_Wz*kG,0?B3-hL % CH_9UW-m7f:1)ymPm]65"~Wmq&DZvY:s$~0P@dhCj`.#{D"kJ+8)}?`nmtb=UqMtZXWC y%{Y 'z1q"aI#O?QKE X aE|e/mP+&dX``ZGj#ju %NzcU&Fv3^#
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