100 Series (NO FOOD, NO WATER, NO STOP)

100 series convergence tests, calculus 2 Here's the file: 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 sum of 1/n diverges, 4:17 2, Sum of 1/ln(n) by The List, 11:10 3, Sum 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 1