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Help me please with this question.

Let $f\in C^{\infty }$ function defined as $\forall x, f(x)=f(x+2\pi )$. Let $e_{n}$ be a summation error of n-segment trapezoidal rule. Prove that $\forall \alpha \geq 0$, $\exists C>0$ so that: $\left | e_{n} \right |\leqslant \frac{C}{n^{\alpha }}$

Thanks a lot!

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