Finding the Limit of a Summation with Infinite Terms

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Homework Statement


∞
lim "sum"(1/n^2)
n→∞ n=0

Can you help me find the final solution?


The Attempt at a Solution



lim (1/n^2) = 0 ?
n-∞

But the "sum" confuses
 
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Lim_{n \rightarrow \infty} \Sigma \left( \frac{1}{n^{2}}\right) So sum each successive term \frac{1}{1}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{4^{2}}+\frac{1}{5^{2}}...
 
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There must be a way to find a final solution (with only one number).
Anybody?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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