Homework Help: Calculus

Posted by Sarah on Thursday, October 20, 2011 at 10:29am.

Find a series ∑a_n for which ∑(a_n)^2 converges but ∑|a_n| diverges

Calculus - Steve, Thursday, October 20, 2011 at 11:32am
Consider
1 - 1/2 + 1/3 - 1/4 + ... (alternating harmonic series)

1 + 1/4 + 1/9 + 1/16 + ... = π²/6

1 + 1/2 + 1/3 + 1/4 + ... diverges (harmonic series)
Calculus - Sarah, Thursday, October 20, 2011 at 12:24pm
thanks!!

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