Proving the monotone decreasing and find the limit ?? Let $a,b$ be positive real number. Set $x_0 =a$ and $x_{n+1}= \frac{1}{x_n^{-1}+b}$ for $n≥0$
(a) Prove that $x_n$ is monotone decreasing.
(b) Prove that the limit exists and find it.
Any help? I don't know where to start.

To prove the limit exists use the fact every decreasing bounded below sequence is convergent. To find the limit just assume $ \lim_{n\to \infty} x_n = x = \lim_{n\to \infty} x_{n+1} $ and solve the equation for $x$
$$ x=\frac{1}{1/x+b} .$$
