October 15th, 2017, 06:33 AM  #1 
Senior Member Joined: Jan 2016 From: Blackpool Posts: 100 Thanks: 2  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! 
October 15th, 2017, 10:12 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 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.
Last edited by v8archie; October 15th, 2017 at 10:17 AM. 

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