 The benefit of introducing the Riemann zeta function is that it can be defined for other values of "s" by analytic continuation.One can then define the zeta-regularized sum of to be "ζ"(−1).From this point, there are a few ways to prove that One method, along the lines of Euler's reasoning, uses the relationship between the Riemann zeta function and the Dirichlet eta function "η"("s").