Convergence for recursive sequence

  • #1

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?
 

Answers and Replies

  • #2
Office_Shredder
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You could compare that series with [tex] \sum \frac{1}{n^2}[/tex]
 

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