Question

My book only goes into details about proving convergence with the alternating series test. How do you prove divergence with it?

Answer 1

@amistre64

Answer 2

if you cant prove it converges, then i would say that it diverges. but thats just a guess.

Answer 3

what are the 2 conditions that prove convergence?

Answer 4

if lim bn = 0 and {bn} is a decreasing series, then sum of an converges

this can be written in the contrapositive as:

if the sum of an diverges, then lim bn not=0 OR {bn} is an increaseing series.

Answer 5

There are 3 conditions: 1. The Un part of the series must always be positive
2. The terms must be getting smaller 3. The terms must be approaching 0