hello, i've stumbled upon another proof. the problem i s:

Prove that if sigma ace of n converges absolutely, then sigma (ace of n)^2 also converges. Then show by giving a counterexample that sigma (ace of n)^2 need not converge if sigma ace of n is only conditionally convergent.

For the first part, can I simply state that if sigma ace of n converges absolutely, it is implied that it converges. If sigma ace of n converges, then the square also converges because p>2 (p-series)?