Comparison Tests [ Direct and Limit]

In this video, I showed how to use both direct comparison test and Limit test . I also explained the necessary conditions for each test to be valid.

[jeffaragon]

I'm just curious about the 2^x at the 8:30 mark. Where did that go when you computed the final form of the derivative?

[kingbeauregard]

There's some sort of test, too, where you divide term "n+1" by term "n", and if that ratio doesn't go to zero, then the series does not converge, right? Or Does that apply only in a limited number of cases? I have only a dim memory of this so I am probably forgetting some important details.