Why $\sum|n^ka_n|<\infty$ implies $f \in C^k$ where $a_n$ is the $n-th$ Fourier coefficient of $f$

Question

I want to know why $$\displaystyle\sum_{n=1}^{\infty}|n^ka_n|<\infty$$ implies $f \in C^k$ where $a_n$ is the $nth$ Fourier coefficient of $f$.

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