If ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an converges, then ∑n=1∞(an+bn)\sum_{n=1}^{\infty} (a_n + b_n)∑n=1∞(an+bn) converges if:
∑bn\sum b_n∑bn converges
∑bn\sum b_n∑bn diverges
bn=1b_n = 1bn=1
bnb_nbn is a constant