# Convergence for recursive sequence

1. Oct 12, 2009

### economist1985

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

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

2. Oct 12, 2009

### Office_Shredder

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