<p>MS, are you sure you're not making fun of us :p ??? (well, i'm sure u are...:D)</p>
<p>i mean, as far as i know, there's no closed formula, which will depend only on n, for<br>
S<em>n=1/1+1/4+1/9+... (\sum</em>{i=1}^n \frac 1{k^2})</p>
<p>There are two ways of proving that lim S_n=pi^2/6:</p>
<ol>
<li>use trigo to place the finite sum between 2 sums which, when n->oo, have the same limit, pi^2/6</li>
</ol>
<p>OR</p>
<ol>
<li>consider f(x)=1/x^2, and write S<em>n as \integral</em>1^n f(x)dx less THE REMINDER... which will come out nicely... </li>
</ol>
<p>so, you are making fun of us, aren't you? :)</p>