# Convergent sequences, limits proof

• April 28th 2011, 03:44 PM
jstarks44444
Convergent sequences, limits proof
Hey all some help with the following proof would be appreciated:

Let L = limit from k to infinity of x-sub-k

If x-sub-k from k=0 to infinity is decreasing, then x-sub-k >= L for all k >= 0

Thanks a bunch!
• April 29th 2011, 03:52 AM
FernandoRevilla
If $x_{k_0} for some $k_0$ , choose

$\epsilon=(L-x_{k_0})/2$

and you'll get a contradiction.