- #1

- 986

- 9

## Homework Statement

Let x

_{1}= √2, x

_{n+1}= √(2+x

_{n}). Use mathematical induction to show that x

_{n}< x

_{n+1}. Next show that if x

_{n}≥ 2, then x

_{n-1}≥ 2 also. How do you conclude from this that x

_{n}≤ 2 for all n? State why lim x

_{n}exists, and find the limit.

## Homework Equations

Upper bounds, limits, etc.

## The Attempt at a Solution

I've done everything up to the point of "find the limit." Help?