Expand the function $\displaystyle f(x)=x\sin{x}$ into Fouriers series on an interval $\displaystyle <-\pi,\pi>$

In my book, the solution of this example starts with.

$\displaystyle f(x)=\sin{x}\sum^{\infty}_{n=1}\frac{2}{n}(-1)^{n+1}\sin{nx}$

I know $\displaystyle b_n$ i 0 because f(x) is an even function. But where did they get the $\displaystyle (-1)^{n+1}$ from? Is that the solution for $\displaystyle a_n$?