Suppose ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an and ∑n=1∞bn\sum_{n=1}^{\infty} b_n∑n=1∞bn converge with an,bn>0a_n, b_n > 0an,bn>0. Which statement must be true?
∑n=1∞anbn\sum_{n=1}^{\infty} a_n b_n∑n=1∞anbn converges
∑n=1∞(an+bn)\sum_{n=1}^{\infty} (a_n + b_n)∑n=1∞(an+bn) converges
∑n=1∞anbn\sum_{n=1}^{\infty} \frac{a_n}{b_n}∑n=1∞bnan converges
∑n=1∞anbn\sum_{n=1}^{\infty} \sqrt{a_n b_n}∑n=1∞anbn converges