$\displaystyle (x_n)_{n\geq 1}, x_1 \in R, x_{n + 1} = \frac {2}{1 + x_n^2}, n \geq 1. $Prove that $\displaystyle \lim_{n\to \infty} = 1$
Thanx
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 $\displaystyle x_1$ is less than that limit) or is decreasing and has a lowwer bound (if $\displaystyle x_1$ is greater than that limit).