3
votes
1answer
83 views

Taylor series with Fibonacci coefficients

Let $\{a_n\}$ be the Fibonacci numbers given by $a_0=0,a_1=1,a_{n+2}=a_{n+1}+a_n$ for $n\geq 0$. Prove that $f(z)=a_0+a_1z+a_2z^2+\ldots$ is a rational function, and determine which rational ...
2
votes
2answers
142 views

Proof That the Ratio of Sucessive N-nacci Numbers Tends to 2.

For the paper that I'm working on involving N-nacci Recursion Formulas I need to prove that $$ \lim_ {n \to \infty}\lim_{a \to \infty} \left | \frac{f^{(n)}_{a+1}}{f^{(n)}_a} \right | = 2$$ To start ...
5
votes
1answer
518 views

N-nacci Identities: The Final Question (Generalizing Time!)

Okay so here is my personal work on the problem set. I only have question 5 remaining which involves generalization of any recursive sequence. $n$'s correspond to the $n$ in n-nacci. I hope to write ...
3
votes
4answers
652 views

Fibonacci( Binet's Formula Derivation)-Revised with work shown

Okay so here is the revised question with my current work. Links to previous post(s)(Just for Gerry): Fibonacci Numbers - Complex Analysis Here's my attempt on the problem set thus far: (Note ...
-2
votes
0answers
175 views

Fibonacci Numbers - Complex Analysis [duplicate]

Possible Duplicate: Complex Analysis - Integral over a circle of radius R Hey guys~ Does anyone know where to find the solutions to this problem set on page 106 involving the fibonacci ...
1
vote
1answer
203 views

Fibonacci Generating Function of a Complex Variable

So I'm doing work on the Fibonacci Numbers, and I came across this problem for the generating function for the recursive fibonacci numbers. I have two questions: 1. Why is it useful to use a ...