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## Converting recursive function to closed form [closed]

Hi, first time here.

My professor gave us a puzzle problem that we discussed in class that I could elaborate on if requested. But I interpreted the puzzle and formed a recursive function to model it which is as follows:

f(n) = n * f(n-1) / (n - 1) + .01, where f(1) = .01 and n is natural


The question that is asked is when (if ever!) does f(x) = 1000x. About half concluded that it eventually will equal (they didn't have the formula I made) and that x would be damn near infinity.

MY personal question is, can that function be reduced so that it isn't recursive? And so that it doesn't need to be solved by brute force computer algorithm (which would be about 3 lines of code).

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I think your question might belong better on math.stackexchange.com - see mathoverflow.net/faq#whatnot – Yemon Choi Feb 4 2011 at 3:41
Will do. Thanks for the tip. To be clear, its not a homework problem, just something I wanted to follow up on. I can see how its not advanced-hardcore-quantum-submanifold theory. – eternalmatt Feb 4 2011 at 4:06