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 ?