I'm asked to show that $\displaystyle \frac{\pi}{4} = \displaystyle \sum^{\infty}_{n = 1} \frac{sin(2n+1)x}{2n+1}$ for $\displaystyle 0 < x < \pi$, but if that were true then the function should be independent of $\displaystyle x$ on the interval... This seems odd. And going to Wolfram|Alpha, it tells me that, at .5, this equality doesn't hold... Am I misunderstand something here? This seems bizarre.