Proof by Example?

  • Thread starter fk378
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  • #1
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Homework Statement


Prove that if a_n>or equal to 0, and sum(a_n) converges, then sum(a_n)^2 also converges.


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?
 

Answers and Replies

  • #2
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I don't think you can prove something by example.
 
  • #3
Dick
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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:

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