Riemann's Zeta function

Question

Possible Duplicate:
Riemann Zeta Function and Analytic Continuation
Calculating the Zeroes of the Riemann-Zeta function

It is stated that Riemann's Zeta function has zeros at negative even numbers.For example if -2 is directly substituted, since the index is in the denominator each term will become a positive number.Then how does the value become zero

Answer 1

The definition $\zeta(s) = \sum{n^{-s}}$ is only valid for $\rm{Re}(s) \gt 1$. Determination of its values for other arguments requires analytic continuation. See: Zeta regularization.