How Can I Calculate the Fourier Series and Use it to Evaluate Infinite Series?

[gomes.]

[PLAIN]http://img69.imageshack.us/img69/6758/123123123nx.jpg

[PLAIN]http://img819.imageshack.us/img819/5390/fsdfsdfsdf.jpg



To calculate the Fourier series, I used the formulae above, and I got:



[PLAIN]http://img831.imageshack.us/img831/2008/xcvxcvxcv.jpg



and i substituted the values into the equation:

[PLAIN]http://img89.imageshack.us/img89/1344/qweqweqwen.jpg



1. So what would my next step be? How do i show that the Fourier series is given by the equation in the questions?



2. and using those results, how do i calculate 1-(1/4)+(1/9)-(1/16)+... and the 1/(n^2) sum to infinity?



Thanks

 

[Hootenanny]

You are done! The series you have given is clearly equivalent to that quoted in the question. If you need to convince yourself, try computing the first few terms of the series.

For the second part: you can compute the first series using the Fourier series you just computed.

 

[gomes.]

thanks!

For the second part: you can compute the first series using the Fourier series you just computed.

thanks, so for the first series, how do i get a final answer?

how would i do the 2nd part?

most appreciated.