# Proof of a limit homework

Tags:
1. Oct 26, 2014

### 3102

1. The problem statement, all variables and given/known data
I have given the statements: $a_{n}^2 \ge x$ , $a_{n+1} \le a_{n}$ , $x > 0$ and $\inf a_{n} > 0$. How to prove the following: $\lim_{n \to \infty}a_{n}=\sqrt{x}$

2. Relevant equations
$a_{n}^2 \ge x$ , $a_{n+1} \le a_{n}$ , $x > 0$ and $\inf a_{n} > 0$
$\lim_{n \to \infty}a_{n}=\sqrt{x}$

3. The attempt at a solution
I have come so far: $$a_{n}\ge a_{n+1} \ge \sqrt{x}$$ How shall I continue?

2. Oct 26, 2014

### PeroK

Are you sure that's the problem? There's not enough information there to show that the limit is $\sqrt{x}$

3. Oct 26, 2014

### HallsofIvy

Staff Emeritus
You can't prove this, it is not true!

For example, a decreasing sequence that converges to $\sqrt{x+ 1}$ will satisfy all the hypotheses of your "theorem".