

Subject:
math problem
Category: Science > Math Asked by: appusavlaga List Price: $3.00 
Posted:
28 Sep 2006 11:27 PDT
Expires: 02 Oct 2006 06:44 PDT Question ID: 769261 
Let f(n) be a function on the nonnegative integers defined recursively as follows: f(0)=1, f(n)=(1+(n*nn)*f(n1))/(n*n+1) for n > 0. So f(1)=1/2, f(2)=2/5 ... This month's puzzle asks for you to determine the asymptotic behavior of f(n) as n > infinity. In other words find a simple function g(x) such that f(n)/g(n) > 1 as n > infinity. 

There is no answer at this time. 

Subject:
Re: math problem
From: barnecaga on 28 Sep 2006 14:59 PDT 
is it cheating to plot the function in excel and look at it? it becomes pretty obvious what the asymptotic behavior is... 
Subject:
Re: math problem
From: yevgenytga on 30 Sep 2006 04:56 PDT 
If we assume that for large n, f(n)~f(n1) then we can change both f(n) and f(n1) to g(n). Solving this equation will give us g(n)=1/(1+n) and it can be verified that indeed this g is one possible solution. 
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