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 \(\displaystyle \lim_{n\to\infty} x_n= \sqrt{k}.\)