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Proof by Example?

  1. Feb 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that if a_n>or equal to 0, and sum(a_n) converges, then sum(a_n)^2 also converges.

    3. The attempt at a solution
    The only example I can think of is 1/(n^p) where p is any exponent greater than 1. Are there any other examples that I can use or do I only need to use this example to prove it?
  2. jcsd
  3. Feb 8, 2008 #2
    I don't think you can prove something by example.
  4. Feb 8, 2008 #3


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    If sum(a_n) converges then there must be an N such that for n>=N, a_n<=1, right? sum(a_n) for n>=N converges. Do a comparison test between a_n and a_n^2 for n>=N.
    Last edited: Feb 8, 2008
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