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!

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- Apr 28th 2011, 03:44 PMjstarks44444Convergent 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! - Apr 29th 2011, 03:52 AMFernandoRevilla
If $\displaystyle x_{k_0}<L$ for some $\displaystyle k_0$ , choose

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

and you'll get a contradiction.