Friday, October 12, 2018

convergence divergence - Why $zeta(-2) $ is not $sum_{n=1}^{infty}frac{1}{n^{-2}}$?

Let $\zeta(s)= \sum_{n=1}^{\infty}\frac{1}{n^{s}}$ a standard formula.



I'm confused if you tell me: does this series: $\sum_{n=1}^{\infty}\frac{1}

{n^{s}}$ converge?



I will answer you: this series is divergent. But if you say: $\zeta(-2)$ it will be: $\zeta(-2)= \sum_{n=1}^{\infty}\frac{1}{n^{-2}}=0$. Will be convergent. So why ?

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