# Convergence or Divergence of a series

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1. Feb 27, 2015

### CourtneyS

1. The problem statement, all variables and given/known data
Does sum from n=1 to n=infinity of 1/[n^(1+1/n)]
converge or diverge.

2. Relevant equations

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

3. 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?

2. Feb 27, 2015

### LCKurtz

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.

Last edited: Feb 27, 2015