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October 15th, 2017, 06:33 AM   #1
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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!
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October 15th, 2017, 10:12 AM   #2
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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.
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Last edited by v8archie; October 15th, 2017 at 10:17 AM.
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