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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.

Thanks in advance.