User:TakuyaMurata/Series

Theorem ''Let $$a_n$$ be a sequence of positive numbers. Then $$\sum_{n \ge 1} a_n$$ converges if and only if $$\prod_{n \ge 1} (1 + a_n)$$ converges.''

Proof:
 * $$\sum_{n \ge 1} a_n \le \prod_{n \ge 1} (1 + a_n) \le \sum_{n \ge 1} e^{a_n}$$ $$\square$$