Convergence or Divergence of a series

[CourtneyS]

Homework Statement

Does sum from n=1 to n=infinity of 1/[n^(1+1/n)]
converge or diverge.

Homework Equations

^^^^^^^^^^^^^^^

The Attempt at a Solution

The general term goes to 0 and its a p-series with p>1, but for large n the series becomes 1/n pretty much so, even tho p>1 is it divergent?

 

[LCKurtz]

Homework Statement

Does sum from n=1 to n=infinity of 1/[n^(1+1/n)]
converge or diverge.

Homework Equations

^^^^^^^^^^^^^^^

The Attempt at a Solution

The general term goes to 0 and its a p-series with p>1, but for large n the series becomes 1/n pretty much so, even tho p>1 is it divergent?

It isn't a $p$ series but, as you say, it's "like" a $p$ series with $p=1$ as $n$ gets large. So if I were you, I would try a limit comparison test with $\sum\frac 1 n$ and see.