# Math Help - limit

1. ## limit

$(x_n)_{n\geq 1}, x_1 \in R, x_{n + 1} = \frac {2}{1 + x_n^2}, n \geq 1.$Prove that $\lim_{n\to \infty} = 1$
Thanx

2. You want to solve...

$L = \frac{2}{1 + L^2}$ where L stands for the limit.

This gives $L^3 + L - 2 = 0$, solve this to find your limit. (factor by (x-1))

3. But I don't need to prove that it is convergent(it has a limit)?

4. Originally Posted by ely_en
But I don't need to prove that it is convergent(it has a limit)?
Yes, you do need to prove that the limit exists. You probably can do that by proving (by induction) that the sequence is increasing and has an upper bound (if $x_1$ is less than that limit) or is decreasing and has a lowwer bound (if $x_1$ is greater than that limit).