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)) ? **

No, there is no such function.

Proof:

(a) Assume such a function exists.

(b) Let x = 0

(c) Then F(0) = 1+F(0), which is not true, not even if F(0) is undefined