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!

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- Oct 17th 2012, 03:09 PMlovesmathBounded and Monotone
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! - Oct 17th 2012, 03:23 PMjohnsomeoneRe: Bounded and Monotone

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. - Oct 21st 2012, 01:31 PMlovesmathRe: Bounded and Monotone
I am having trouble proving by induction. How should I set that up?

- Oct 21st 2012, 03:07 PMjohnsomeoneRe: Bounded and Monotone

- Oct 21st 2012, 03:55 PMlovesmathRe: Bounded and Monotone
This helped so much. I was able to see where I went wrong. Thanks!