Absolute convergence of $\sum a_n$

Question

I would ask a help for the following problem If someone could tell me what criteria or applies so I would appreciate. Show that if $ \sum \limits^{\infty }_{n=1}a_n $ is absolutely convergent, then $ \sum \limits^{\infty }_{n=1}(a_n)^{2} $ is convergent and Give an example to show that the converse is false

Answer 1

Hint: If $\sum|a_n|$ converges, then $a_n^2 \leqslant |a_n| < 1$ for $n$ sufficiently large.