Math Help - Fourier Series

1. Fourier Series

solved thanks

2. Originally Posted by gomes

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

and i substituted the values into the equation:

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

You may want to open up the sum you got: it's exactly the same as in the question, so you already have (1)

As for (2): according to what you wrote: $0=f(0)=\frac{\pi^2}{3}+4\sum\limits^\infty_{n=1}\f rac{(-1)^n}{n^2}\Longrightarrow \sum\limits^\infty_{n=1}\frac{(-1)^{n-1}}{n^2}=\frac{\pi^2}{12}$.

Likewise: $\pi^2=f(\pi)=\frac{\pi^2}{3}+4\sum\limits^\infty_{ n=1}\frac{1}{n^2}\Longrightarrow$ ....get the sum

Tonio