Let $(c_n)$ be a decreasing sequence of positive numbers. If $\sum c_n \sin nx$ is uniformly convergent, then how to show that $\lim_{n\to\infty} n c_n = 0$?
2026-04-30 04:55:55.1777524955
A Result About Sequences And Series
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Hint: If $\sum u_n$ be a convergent series of positive real numbers and $\{u_n\}$ is a monotone decreasing sequence then $\lim_{n\rightarrow\infty} nu_n=0$