# Max of sum of sines

Hi!

Consider the function

$\frac{d^n}{dx^n} \sum_{k=1}^m \sin{kx}, \quad 0 \leq x \leq \pi/2$.

If $n$ is odd this function attains its largest value, $\sum_{k=1}^m k^n$ at $x=0$. But what about if $n$ is even? Where does the maximum occur and what value does it take?

Any help is much appreciated. Thank you!

Last edited: