Question

Let {an} and {bn} be sequences such that {an} diverges to infinity and {bn} is bounded. Prove that {an + bn} diverges to infinity.

Since {bn} is bounded, there exists a positive integer M such that abs value (bn) <= M (or -M <= bn <= M). Since {an} diverges to infinity(positive), for all M, there exists an N such that if n >= N, an > M. I've gotten this far, but not entirely sure how to proceed.

Answer 1

you can use the same N as you do for \(a_n\) or if \(b_n\) is bounded below by M then \(M+N\)

Answer 2

I'm just having trouble setting up the inequality for {an + bn}