I'm looking for the asymptotic approximation of the product of the first $n$ Fibonacci numbers.

Does there exist a tight approximation for these kind of things?

  • 5
    $\begingroup$ Better start at $F_1$, not $F_0=0$... $\endgroup$ – lhf Jun 13 '16 at 19:19

By the Binet formula,


Then multiplying the $n$ first estimates

$$P_n\approx a\frac{\phi^{n(n+1)/2}}{\sqrt5^n}.$$

By numerical computation, $a\approx 1.22674201072$.

We can deduce an expression for the geometric average


| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.