Infinite Series Test: 1/n^2 - 1/n^3

[renob]

Homework Statement

\sum^{infinity}_{n=1} (1/n^2 - 1/n^3)

Homework Equations

it goes to infinity
n=1

The Attempt at a Solution

Im assuming this is a telescoping series. when I plugged in my terms nothing canceled out except for the 1's at the beginning.

(1-1)+(1/4 - 1/8)+(1/9 - 1/27)+...

Am I doing something wrong? Or does it just go to infinity and therefore diverge?

 

[Mark44]

You didn't say what you're supposed to do with this series, which would have been useful information.

Presumably you're supposed to determine that the series is divergent or it is convergent. What tests do you know of that you can use?

When you ask "does it just go to infinity", what are you referring to by "it"? Whatever "it" is, why do you think "it" goes to infinity? There's nothing in the work you show that suggests that to me.