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Is (1 - 2/2^s)f(s)= 1 -1/2^s + 1/3^s - 1/4^s ... a valid definition of riemann zeta in [1,∞)

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Once again your question is not of research level. It belongs to a first course in analytic number theory or complex analysis. Try math.stackexchange.com instead, or read a textbook. All questions of this sort will be closed. – GH Mar 7 2012 at 15:55

closed as not a real question by Vladimir Dotsenko, Felipe Voloch, quid, GH, Tom Leinster Mar 7 2012 at 15:56

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