Is my proof for "Absolute convergence => Convergence" right? I had to prove it for my calc test today; my proof looks different than the one my prof posted as the answer; it's also way shorter. He used the one from the book but I didn't memorize it so I used this. Is it right? 1. The problem statement, all variables and given/known data Prove that Absolute Convergence implies convergence 3. The attempt at a solution Notation: 1. I'm using the notation an means a series. [As in: an = a(1)+a(2)+a(3)...+a(n) and n goes to infinity] 2. |an| means the absolute value of |an|. *** I. |(-1)^n an| = an. II. Suppose an converges. i.e: an = C III. an converges implies that a(n+1) < a(n) IV. (III.) implies (-1)^n an converges. QED.