Infinite series, convergence?

Question

If we know that An > 0 and The sum from 1 to infinity of An is convergent how do you prove that the sum from 1 to infinity of An squared is also convergent?

Answer 1

i think in order that series to be convergent An should converge to 0. Now that means that, at least from some index on, An will have values less than 1, But
0

Answer 2

if S (An) is convergent lim An =0 ( necessary condition) so certainly An<1. So An^2