Let $\displaystyle (c_n)$ be a decreasing sequence of positive numbers.If $\displaystyle \sum c_n sin nx$ is uniformly convergent, show that $\displaystyle lim (n c_n) = 0$.

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- Dec 16th 2009, 02:50 AMproblemUniformly convergent sequence
Let $\displaystyle (c_n)$ be a decreasing sequence of positive numbers.If $\displaystyle \sum c_n sin nx$ is uniformly convergent, show that $\displaystyle lim (n c_n) = 0$.

- Dec 16th 2009, 08:50 PMproblem
Can anyone give me any hints?

Thanks!