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September 15th, 2007, 08:13 PM   #1
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Fibonacci & Prime Numbers

Let F(n) be an function for Fibonacci numbers, and let P(n) be an function for prime numbers. Then, evaluate
limx->inf (F(n)/P(n)). Is this possible, or is this impossible to evaluate?
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September 16th, 2007, 02:25 AM   #2
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I supose that "the function for prime numbers" is a function that would for any n E Integers return the n-th prime? If so, then asymptoticly it can be approximated with P(n)=C*n*ln(n) where C is a constant (not sure what it equals, but it's Real and >0) Now,
F(n)= 1/sqr(5)*(((1+sqr(5))/2)^n-((1-sqr(5))/2)^n)

you can see that the Fibonacci sequence grows with an exponential rate, and the prime numbers function at a lower rate, so the limF(n)/P(n),n->00 =+00
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September 16th, 2007, 06:44 AM   #3
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Heck, the Prime Number Theorem is overkill -- even knowing that p_n is O(n^k) for some k suffices.
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