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What is the exact value of this

Mathematics
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|dw:1356270940251:dw|
\(\huge \frac{\pi^2}{6}\)
how?

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Other answers:

which method do u want? i know the one using Fourier Transform...
Any easy method.... I havent learn Fourier Transform
btw, you can write your question with the equation buttom, then you can copy the script and paste it to the question box, it will emerge as an equation :)
U can do it using Fourier Transform .... I will try to catch it
Fourier Series expansion for f(x) in [0,2pi] \(f(x)=a_0/2+\sum \limits_{n=1}^\infty a_n\cos nx+\sum \limits_{n=1}^\infty b_n\sin nx\) \[a_0=(1/\pi)\int \limits_0^{2\pi}f(x)dx\] \[a_n=(1/\pi)\int \limits_0^{2\pi}f(x)\cos nxdx\] \[a_0=(1/\pi)\int \limits_0^{2\pi}f(x)\sin nxdx\]
here, use \(f(x)=(\frac{\pi-x}{2})^2\)
and find Fourier series Expansion of f(x) u should get, bn=0 an=1/n^2
sorry, the last one is bn \[b_n=(1/\pi)\int \limits_0^{2\pi}f(x)\sin nxdx\]
this really is the longer way to do it...
Thanx for the reply will see it later

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