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What is the Sum of negative integers of zeta function? $$ \sum_{s=1}^{\infty} \zeta(-s) = \zeta(-1) + \zeta(-2) + \zeta(-3) + \zeta(-4) + ... $$ The negative even number of the zeta function is zero. and the negative odd number appears alternately. It is likely that there will be some value in analytical continuation.

Thank you.

  • Likely or not: why do you think that would be important? Can you think of any (real world or inner-mathematical) problem resulting in such a sum? –  Jun 19 '17 at 07:50

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