Limit of a Recursive Expression

Calculus Level 2

True or False?

For any real k>0,k >0, given the recursive expression
xn=xn1+kxn1+1,x_{n} = \frac{x_{n-1}+k}{x_{n-1}+1}, if x0=0,x_0 = 0, then limnxn=k.\displaystyle \lim_{n\to\infty} x_n= \sqrt{k}.

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