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

• Feb 16th 2011, 08:53 PM
gwiz
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?
• Feb 16th 2011, 09:02 PM
CaptainBlack
Quote:

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