Cesaro summable implies that $c_{n}/n$ goes to $0$
Hint: Cesàro summable means that $\lim_{n\to\infty}\frac{c_1+\cdots+c_n}n$ exists. Note that $\frac{c_1+\cdots+c_n}n = \frac{c_1+\cdots+c_{n-1}}{n-1}\cdot(1-\frac1n)+\frac{c_n}n$.
Cesaro summable implies that $c_{n}/n$ goes to $0$
Hint: Cesàro summable means that $\lim_{n\to\infty}\frac{c_1+\cdots+c_n}n$ exists. Note that $\frac{c_1+\cdots+c_n}n = \frac{c_1+\cdots+c_{n-1}}{n-1}\cdot(1-\frac1n)+\frac{c_n}n$.