Friday, May 20, 2016

real analysis - Is sum+inftyn=1left(frac1nfrac1pnright) convergent?

It is known that +n=11n is divergent. Also, it is known that +n=11pn is divergent where pn is n-th prime number.



I was thinking what would happen (in the sense of convergence) if we termwise subtract these two series to obtain +n=1(1n1pn)



Is +n=1(1n1pn) convergent?

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