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I'm trying to prove that

[tex]\sum_{n=1}^\infty \frac{1}{n^s} = \prod_{p} (1-p^ {-s} )^ {-1} [/tex]

I know why it is and a proof, but I'm actually looking for

a different way to prove going backward and deriving the

sum from the product of primes. Can you show me a way to do that?

I'd like to start with...

[tex] \prod_{p} (1-p^ {-s} )^ {-1} = ... [/tex]

Thanks,

p.s that -s above and then following -1 should be both exponents for the equation

same with -s and -1 on the bottom, I'm not the master latex writer. Can somebody also tell me why it doesn't work?

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# Proving the golden key,

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