On page 168 of Mathematical Fallacies and Paradoxes, it states that the fact that the series

$1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots $

has a sum depends on the Axiom of Choice. Where does the AC come in to play? I know that if the terms are permuted, we can get any sum we want, and I can see how the AC might be involved there, but just the fact that $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots $ converges?