## anonymous 3 years ago What is the exact value of this

1. anonymous

|dw:1356270940251:dw|

2. hartnn

$$\huge \frac{\pi^2}{6}$$

3. anonymous

how?

4. hartnn

which method do u want? i know the one using Fourier Transform...

5. anonymous

Any easy method.... I havent learn Fourier Transform

6. anonymous

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 :)

7. anonymous

U can do it using Fourier Transform .... I will try to catch it

8. hartnn

Fourier Series expansion for f(x) in [0,2pi] $$f(x)=a_0/2+\sum \limits_{n=1}^\infty a_n\cos nx+\sum \limits_{n=1}^\infty b_n\sin nx$$ $a_0=(1/\pi)\int \limits_0^{2\pi}f(x)dx$ $a_n=(1/\pi)\int \limits_0^{2\pi}f(x)\cos nxdx$ $a_0=(1/\pi)\int \limits_0^{2\pi}f(x)\sin nxdx$

9. hartnn

here, use $$f(x)=(\frac{\pi-x}{2})^2$$

10. hartnn

and find Fourier series Expansion of f(x) u should get, bn=0 an=1/n^2

11. hartnn

sorry, the last one is bn $b_n=(1/\pi)\int \limits_0^{2\pi}f(x)\sin nxdx$

12. hartnn

this really is the longer way to do it...

13. anonymous

Thanx for the reply will see it later