# Riemann Zeta Function Z(z)

I was wondering how do you calculate the Riemann value, of a Riemann Zeta Function, for example the riemann zeta function for n = 0, is -1/2, which envolves a bernoulli number (what is a bernoulli number and what roll does it play in the Riemann Zeta Function), can anyone explain that to me? Also what do you apply the riemann zeta function to, besides Quantum Mechanics.

And also how do you go about finding the sum of a series (non geometrical)?

$$\zeta(2n)=\frac{(-1)^{n+1}B_{2n}(2\pi)^2^n}{(2)(2n)!}$$

$$\frac{\pi^2}{6}=\sum_{n=1}^\infty \frac{1}{n^2}$$

Specifically, this one I want to know the proof for this sum, can anyone nice enough out there, please show me!
Step by step process

Last edited: