I need to know if the following series converges:(adsbygoogle = window.adsbygoogle || []).push({});

∑(k=1 to k=oo)[(((-1)^k) ζ(k))/(e^k)]

The problem is that zeta(1)=oo; however, the equation satisfies the conditions of convergence for an alternating series [the limit as k->oo=0 and each term is smaller than the last.]

Any thoughts?

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# Zeta function and summation convergence

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