Dirichlet test for convergence

[jtn2007]

Homework Statement

use dirichlet test to determine if the series converges 1-1/2-1/3+1/4+1/5-1/6-1/7+...

Homework Equations

The Attempt at a Solution

I have broken up the series into two different series the first series I have is
1+1/4+1/8+1/12+... and the second series I have is -1/2-1/3+1/5-1/6-1/7+...

I'm not even sure if these are the two correct series to break it up into, but I know I need to determine if one is bounded and the other is decreasing and limit convergent to 0. Any help is great.

 

[Dick]

You can't split up the series like that unless you already know it's absolutely convergent. And I really don't see why you would want to. To apply the dirichlet test you want to factor the series. Let a_n={1,1/2,1/3,1/4...}. What series would you MULTIPLY that by to get the original series?