How can I solve this problem?
In order to build a function whose Fourier series is convergent but not uniformly convergent, The following series needs to be accurately estimated.
Using the formula $\frac{\pi - x}{2} = \sum_{k=1}^{\infty} k^{-1} \sin kx, 0 \lt x \lt 2\pi$, show that $\forall$$x$ and $n$$$|\frac{\sin x}{1} + \frac{\sin 2x}{2} + ... + \frac{\sin nx}{n}| \leq \frac{\pi}{2} + 1$$