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Get ready to dive into the world of infinite series with this exciting video! We'll cover 100 different series and use 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. This is the perfect opportunity to enhance your understanding of calculus and solidify your knowledge of these essential series. Whether you're a student struggling to keep up with your calculus 2 class or a curious learner looking to delve deeper into math, this video is perfect for you. Plus, don't miss out on the chance to get a hoodie and show off your love for calculus 👉 . Join us on the BlackPenRedPen YouTube channel for an unforgettable journey through Infinite series. Get a Convergence t-shirt: 👉 Try the problems first: 👉 Check out my other “100-everything“ series: 100 Derivatives: 100 Integrals: 100 Series: 100 Calculus 2 Problems: *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
