A trigono inequality

[Румен Симеонов]

Let $p\in[1,+\infty)$, and $2\leqq n\in \mathbb{N}$. Prove that:
$n\leqq 2^p\sum_{k=1}^{n-1}sin^p \left(\frac{k\pi}{n}\right)$.

[jimbos]

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