Calculus II: Comparison test

In this video, we talk about the comparison test, one of the methods used to determine convergence/divergence of a series.

00:00 - Introduction
00:15 - Definition of the comparison test
03:53 - Example 1
05:48 - Example 2
07:44 - Example 3
10:19 - Example 4

[pschymit]

In Ex 2, you mentioned cos(n) > 0. I thought “why can’t cos^2(n) = 0 as well, in which case we should say that n/( n^2 - n ) is >= n/(n^2), not > . However, I realised this is because n is a natural number and cos^2(x) is zero only when x is a multiple of pi.

[alanha]

can u explain why 1/n would diverge? it continuously goes smaller and smaller wouldnt it converges as the limit goes to infinity for example 2

[rishavroy]

Hey what did you mean by a p series? In the third example