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.

Printable View

- Oct 3rd 2011, 06:29 PMjsmith90210Two 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.

- Oct 3rd 2011, 06:59 PMMonroeYoderRe: 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?