Saturday, 8 April 2017

Series convergence sumlimits+inftyk=1ka2k

I found a nice problem about series convergence. And would like to share it.



Suppose series +k=1ak converges absolutely.



1) Found an example when +k=1ka2k diverges.




2) Suppose that ak is a non increasing sequence. Is it true that +k=1ka2k converges?



3) Is it true that if ak is a non increasing then +k=1k2a2k converges?

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