I currently have the equation:
$ \lim_\limits{n\to\infty}(X_{n+1}) = \lim_\limits{n\to\infty}(X_n)^2 $
I am simply looking for just the limit of $X_n$ so can I simply square both sides and have:
$ \lim_\limits{n\to\infty}(X_n) = \lim_\limits{n\to\infty}(\sqrt{X_{n+1}}) $
Thanks to whoever can clarify this for me!
EDIT: Sorry guys, formatting is fixed now, it's a recursive sequence.
You can do that but there is no reason to- changing from the square to the square root doesn't help. If this sequence converges, let X be the limit. Then taking the limit as n goes to infinity of both sides gives $X= X^2$ so that $X^2- X= X(X-1)= 0$, either X= 0 or X= 1. Whether the sequence converges and, if so, which of those is the limit depends on what the initial value is. Obviously if $X_0= 0$, the sequence is 0, 0, 0, ..., which converges to 0 while if $X_0= 1$, the sequence is 1, 1, 1,..., which converges to 1. In fact if is not difficult to see if $|X_0|> 1$, the sequence does not converge, if $|X_0|= 1$ the sequence converges to 1, and if $|X_0|< 1$ the sequence converges to 0.