Suppose a0>1 and an(read: a sub n)=2-1/a(sub n-1), n is an element of the natural numbers. Show that the sequence {a(sub n)} from n=1 to infinity is bounded and monotone. Find the limit.
Help, please!
It's almost always enlightening to simply write out the first few when given a recurrence formula:
It's pretty obvious that the general form will be:
Prove it by induction.
Then the monotinicity is just a matter of algebra, and the limit is easy to compute.