Youtor
Ratio Test
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How to do the series convergence tests for your Calculus 2 class. You will learn all types of convergence tests including direct comparison, telescoping series, limit comparison test, ratio test, root test, p-series, geometric series, and more! Best wishes for your calculus 2 class! • Get a Convergence t-shirt: 👉 https://www.amazon.com/dp/B0C54H5TZV • Try the problems first: 👉 / files-to-my-100-95153770 • Check out my other 100-everything series: • 100 Derivatives: • 100 calculus derivatives (in one take) • 100 Integrals: • 100 integrals (world record?) • 100 Series: • 100 series convergence tests (no food... • 100 Calculus 2 Problems: • 100 calculus 2 problems! (ultimate fi... • 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
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