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Theorem.

If $\sum_{n=1}^{\infty}c_{n}$ is Cesaro summable, then $c_{n}/n$ tends to $0$.

How to prove it?

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    Please consider edit your post according to what you want to ask2012-10-06

1 Answers 1

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Hint: Cesàro summable means that $\lim_{n\to\infty}\frac{c_1+\cdots+c_n}n$ exists. Note that $\frac{c_1+\cdots+c_n}n = \frac{c_1+\cdots+c_{n-1}}{n-1}\cdot(1-\frac1n)+\frac{c_n}n$.

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    Thank you for your advice!2012-10-06