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I appologise in advance. My maths knowledge is pretty bad, so some of what I say may not make sense.

I'm interested in the Riemann Zeta function, and more specificaly, the Riemann zero's. I'm not trying to prove it, I just want to calculate some of the values. And that's what I'm having trouble with. I'm okay with complex numbers, but I'm struggling with the series. For example, if I have:

zeta(1/2 + 10i) = sigma(1 / n^(1/2 + 10i)) for n=1 to infinity

I can calculate the values for specific values of n, but n goes all the way to infinity. So, to actually calculate the final value of zeta(1/2 + 10i) I guess I need to use somesort of convergence check. Am I right in thinking this? And, could using somesort of convergence check allow me to calculate a final value for zeta(1/2 + 10i)? Could someone show me how to calculate the final value or point me in the right direction?

Thanks ,