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| Name | 100 series convergence tests (no food, no water, no stop) |
| Video Uploader | Video From blackpenredpen |
| Upload Date | This Video Uploaded At 06-05-2019 19:56:03 |
| Video Discription | 100 infinite series and series convergence tests. All the convergence tests you need to know for your Calculus 2 class, including direct comparison, telescoping series, limit comparison test, ratio test, root test, p-series, geometric series, and more! Get a Convergence t-shirt: 👉 https://www.amazon.com/dp/B0C54H5TZV Try the problems first: 👉 https://www.patreon.com/posts/files-to-my-100-95153770? Check out my other "100-everything" series: 100 Derivatives: https://youtu.be/AegzQ_dip8k 100 Integrals: https://youtu.be/dgm4-3-Iv3s 100 Series: https://youtu.be/jTuTEcwvkP4 100 Calculus 2 Problems: https://youtu.be/Kwyk_mteyNc *mistakes* Thanks to several viewers, at Q25, 1:53:40 , n should go from "2" to inf. And in that case, cos(pi*n) will produce 1,-1,1,-1,... but it is still a convergent alternating series. Thanks to Chester, at 2:34:35, I meant to say 1/3 is less than "1", not 0. So we can draw a conclusion from the Ratio Test. Thanks to Alberto! At 4:52:58 the final answer should be x is less than “-1” Highlights: (see pinned comment for ALL timestamps) start: 0:00 1, Classic proof that the series of 1/n diverges, 4:17 2, series of 1/ln(n) by The List, 11:10 3, series of 1/(ln(n^n)) by Integral Test, 17:05 4, Sum of 1/(ln(n))^ln(n) by Direct Comparison Test, 22:45 9, Sum of (-1)^n/sqrt(n+1) by Alternating Series Test, 49:10 15, Sum of n^n/(n!)^2 by Ratio Test, 1:22:20 16, Sum of n*sin(1/n) by Test for Divergence from The Limit, 1:28:04 26, Sum of (2n+1)^n/n^(2n) by Root Test, 1:58:11 30, Sum of n/2^n, 2:10:40 32, Sum of 1/n^(1+1/n), 2:22:30 41 to 49, true/false: 2:52:58 90, Sum of (-1)^n/n! = 1/e by Power Series, 5:24:40 100, Alternating Harmonic Series 1-1/2+1/3-1/4+1/5-... converges to ln(2) by Power Series, 5:54:40 101, Series of 3^n*n!/n^n by Ratio Test, 6:00:00 #100series #calculus #satisfying #apcalculus #gcse May 6th, 2019 |
| Category | Education |
| Tags | 100 series | Series Convergence Tests | series of 1/ln(n) | sum of 1/(n*ln(n)) | calculus 2 series convergence tests | sum of 1/ln(n^n) | 100 infinite series | integral test for series | telescoping series | sum of n/2^n | blackpenredpen | converge or diverge | blackpenredpen best friend | test for convergent series | calculus 2 tutorial | 100 calculus 2 series | calculus 2 sequence and series | ratio test | root test | direct comparison test | series of 1/n | classic proof for series of 1/n |
