# Math Help - Proving convergence of {an/bn} given...

1. ## Proving convergence of {an/bn} given...

Theorem: If {an} is bounded and {bn} tends to infinity with bn not equal to 0 for all n, then {an/bn} converges to 0.

I am having trouble understanding why this theorem is true. Can somebody please provide me with a proof?

2. Originally Posted by gwiz
Theorem: If {an} is bounded and {bn} tends to infinity with bn not equal to 0 for all n, then {an/bn} converges to 0.

I am having trouble understanding why this theorem is true. Can somebody please provide me with a proof?
$-\dfrac{K}{|b_n|}\le \left| \dfrac{a_n}{b_b} \right| \le \dfrac{K}{|b_n|}$

where $K \ge |a_n|$ for all $n \in \mathbb{N}$

CB