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 Maybe? (Posted on 2012-01-15)
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)) ?

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 Nearly correct answer (spoiler) | Comment 2 of 3 |
F(x) = -1/x nearly does it, and I suspect that this is what Ady was expecting as an answer.

For every x, except for -1 and 0 (and even for x < -1), it is then true that F(x) = 1+ F(x/(x+1))

Proof:
1+ F(x/(x+1)) = 1-(x+1)/x = -1/x = F(x)

Of course, F(x/(x+1)) is undefined if x = -1 or 0.  As previously noted, we cannot possibly assign F(0) a value such that F(0) = 1+F(0).  So this function does not satisfy the problem statement.

If only the problem had said that the sought-after relationship was true for all x except -1 and 0, then I could have solved it.  Ah, regrets.

Edited on January 15, 2012, 10:25 pm
 Posted by Steve Herman on 2012-01-15 21:10:03

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