Proof that zeta(-1) is -1/12

1. Jan 17, 2014

bgq

Hi,
I have read that zeta(x) = 1^(-x) + 2^(-x) + 3^(-x) + ... infinity
for x = -1, zeta(-1) = 1 + 2 + 3 + 4 + 5 ...
What confused me is that zeta(-1) = -1/12 and so 1 + 2 + 3 + 4 + 5 + ... = -1/12
Can anybody give a proof that zeta(-1) is -1/12.

2. Jan 17, 2014

Office_Shredder

Staff Emeritus
The main gist is that $\zeta(x)$ is a function such that if x>1,
$$\zeta(x) = 1^{-x} + 2^{-x} +....$$