Limit of a Recursive Expression

Calculus Level 2

True or False?

For any real $$k >0,$$ given the recursive expression
$x_{n} = \frac{x_{n-1}+k}{x_{n-1}+1},$ if $$x_0 = 0,$$ then $$\displaystyle \lim_{n\to\infty} x_n= \sqrt{k}.$$

×