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Homework Statement
Prove that if a_n>=0 and summation a_n converges, then summation (a_n)^2 also converges.
The Attempt at a Solution
(Note: When I say "lim" please assume the limit as n-->infinity). I just want it to be a little clearer to read)
If summation a_n converges, then lim(a_n)=0. If lim(a_n)=0, then lim(a_n)^2=0.
If summation (a_n)^2 diverges, then lim(a_n)^2 does not equal 0. But lim(a_n)^2=0, so summation (a_n)^2 must converge.
Can anyone let me know if this is a valid proof? I'm not sure how else to prove it otherwise...thank you.
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