Figuring out whether a series converges or not

[eventob]

Homework Statement

I am supposed to show whether the series converges or diverges. I guess I need to use the ratio test … at least my calculus professor told us that we should use that test whenever we had complicated terms like n! and such.

Homework Equations

lim_n->inf a_(n+1)/a_n = L
If L<1 the series converges, if L>1 it diverges and if L=0 ... who knows? :p

The Attempt at a Solution

I tried to do the problem, but I am not sure if I got it right or not. My attempt at a solution is attached, along with the problem, in the image.


Thanks in advance.

 

[Dick]

Sure. The ratio test gives you 0. It converges.

 

[Mark44]

Homework Equations

lim_n->inf a_(n+1)/a_n = L
If L<1 the series converges, if L>1 it diverges and if L=0 ... who knows? :p

0 < 1, so if L = 0 in the Ratio Test, the series converges.