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Consider the function

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

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

Any help is much appreciated. Thank you!

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# Max of sum of sines

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