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)

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.

anonymous · Answer

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

tiffany_rhodes · Answer

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