Is it true that $ \sum_{n=1}^{\infty}\sqrt{a_{n}} $ converge $ \Rightarrow\sum_{n=1}^{\infty}a_{n} $ converge?
$\sum_\limits{n=0}^{\infty} a_n$ converges $\implies \sum_\limits{n=0}^{\infty} a_n^2$ converges