Thread: Sequence and limit

Let xn be a sequence of real numbers satisfying xn+1≤xn for n=1,2,...
Assume there is a constant c such that xn>c-1/n.
Show that l=lim(xn) exists and l>c

Originally Posted by ashamrock415

Let xn be a sequence of real numbers satisfying xn+1≤xn for n=1,2,...
Assume there is a constant c such that xn>c-1/n.
Show that l=lim(xn) exists and l>c

is a monotone decreasing sequence, and as , we get that this sequence is bounded from below

and thus exists.

All is left is to show that is actually this sequence's infimum...

Tonio