My Math Forum sequence question

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 October 15th, 2017, 06:33 AM #1 Member   Joined: Jan 2016 From: Blackpool Posts: 59 Thanks: 1 sequence question find a sequence an such that sum of an is convergent but sum of an^2 is divergent??? This is confusing me a lot please could someone give me a tip, thanks! Thanks from topsquark
 October 15th, 2017, 10:12 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,034 Thanks: 2342 Math Focus: Mainly analysis and algebra Remember that the terms $a_n$ can be negative as well as positive. You can then select your $a_n$ such that $\sum a_n$ and $\sum (-1)^n a_n^2$ are conditionally convergent, and thus $\sum a_n^2$ is not convergent because every term is positive. Thanks from topsquark and Jaket1 Last edited by v8archie; October 15th, 2017 at 10:17 AM.

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