Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ Iam stuck with this proof. There seems to be no property to help.
If $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ and that the reverse isnt true.

$\sum_1^\infty{a_n^2} \leq (\sum_1^\infty|a_n|)(\sum_1^\infty|a_n|) < \infty$
A example to show reverse untrue.
See $a_n = \frac {1}{n} $
