Solution
= Solution
Evaluate at $x=\pi/2$, where the original expression gives $f(\pi/2)=1-\pi^2/4$. The <Fourier series> gives
$$
1-\frac{\pi^2}{4}=1-\frac{\pi^2}{6}
+\sum_{m=1}^\infty\frac{(-1)^m}{m^2}.
$$
Rearranging proves
$$
\boxed{\sum_{m=1}^\infty\frac{(-1)^m}{m^2}=-\frac{\pi^2}{12}}.
$$
The convergence at this point is justified by the continuity properties noted in part (b).