sequences and series - How to calculate $S_{n}=sum_{i=1}^{n}frac{1}{i^{2}}$

In math lesson, my teacher told me that Euler once used a very delicate method to calculate $\displaystyle S_{n}=\sum_{i=1}^{n}\frac{1}{i^{2}}$ and wrote a paper about it.

I wonder how to calculate this. I need a precise answer, not the answer that it's less than a number such as 2.