- #1

- 65

- 0

## Homework Statement

If X

_{n}is bounded by 2, and [tex]|X_{n+2} - X_{n+1}| \leq \frac{|X^2_{n+1} - X^2_n|}{8} [/tex], prove that X

_{n}is a convergent sequence.

## Homework Equations

## The Attempt at a Solution

I believe the solution lies in proving X

_{n}a Cauchy sequence, but I'm not sure how to work it out. I considered |X

_{n}- X

_{m}| adding and subtracting the terms between m and n but i got stuck.

I also tried to check for telescoping, with no luck.

Last edited: