Suppose x_{1}>0, and consider the sequence, $\{x_{n}\}$ defined as follows: $x_{n+1}=\log(1+x_{n}) \quad n\geq 1 $ Find the value of $\displaystyle \lim_{n \to \infty} nx_{n}$
I am having trouble solving it. One thing is clear, that since x_{n}>0 and $x_{n+1} < x_{n}$, we can have a sequence which converges an $f$ which satisfies $f=\log(1+f)$, so that $f=0$. Any way as to how we can proceed from here.