Riemann Zeta Function (Part 1, beware)

Calculus Level 3

The Riemann zeta function states that for every s s ,

ζ ( s ) = n = 1 1 n s \large \zeta (s) = \sum_{n=1}^\infty \frac {1}{n^{s}}

Sometimes these sums are divergent but using analytic continuation, you can get a finite answer. Find ζ ( 0 ) \zeta (0) .


The answer is -0.5.

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1 solution

Anand Raj
Jun 23, 2014

S = 1+1+1+1+1+1+1+...........

Let X=1-1+1-1+1-1+1-1+..................( equals 1/2)

Then S + X = 2S S = -1/2

I think it should be S - X = 2S . Therefore S = -X = -1/2 . (That's the way i did it, but i think we both might be wrong)

Aakarshit Uppal - 6 years, 11 months ago

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