Is there a function
F(x), such that for every x, larger than -1, the following is true:

** F(x)=1+ F(x/(x+1)) ? **

(In reply to

Nearly correct answer (spoiler) by Steve Herman)

I maintain that your 1st answer is the right one: **there is no such function,** and you've explained it loud and clear. X=0 prevents stating : "for all x ... "etc.

Nevertheless nothing's wrong with your additinal observations about "almost every x .." etc.

**No regrets!!**