# Math Help - Two convergent subsequences, divergent sequence

1. ## Two convergent subsequences, divergent sequence

I know that if a sequence has two subsequences that converge to different values than that sequence is divergent. However, I am asked to prove this fact. Any help is much appreciated.

2. ## Re: Two convergent subsequences, divergent sequence

The basic setup is to let two subsequences converge to two different values. Then to show the sequence doesn't converge, take a particular epsilon and show that you for all N sufficiently huge you can't be close to one limit value because you must be hitting the limits of the subsequences

Can you see a good epsilon to choose?