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Homework Help: Convergence for recursive sequence

  1. Oct 12, 2009 #1
    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. jcsd
  3. Oct 12, 2009 #2


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    Staff Emeritus
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    Gold Member

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