let $a_1$ be an arbitrary postive number and let $a_{n+1} = \log (1+a_n) $ for $n \ge 1$. Check whether $\sum_{n=1}^{\infty} a_n$ converges or diverges?
My attempt: I know that $\log(1+x) = x - \frac{x^2}{2} + \frac {x^3}{3} \cdots$
Now here how can I conlcude that $\sum_{n=1}^{\infty} a_n$ converges or diverges?
Any hints/solution will be appreciated.