Convergence for recursive sequence

[economist1985]

Homework Statement

Let x_1=1 and let x_n=x_n-1 + 1/n^n for n>1. Show that x1, x2, ... is convergent.

Homework Equations

The Attempt at a Solution

I have managed to transform x_n=summation(1/n^n). How do I show that this is convergent?

 

[Office_Shredder]

You could compare that series with $$\sum \frac{1}{n^2}$$