Ex: Infinite Series - Direct Comparison Test (Convergent)

This video provides an example of how to apply the direct comparison test to determine if an infinite series is convergent, divergent, or if the test is inconclusive.

[calcubite]

3:00 The n is positive for all n. So we can cross multiply the inequality without changing the direction of the inequality. Why cannot we simply say n^ <= (n^6+5)
You are doing the beginning of a proof by mathematical induction by presenting a few base cases from 2:45 through 4:28, but this doesn't seem necessary. Is it though?

[liangpingshen]

@0:56, how did 1/n^2 come to play a role?