How to show that this binomial sum satisfies the Fibonacci relation?
8 May 2025 at 2:22am
Fibonacci sequence, strings without 00, and binomial coefficient sums. 1. Proof of the relationship ...
Fibonacci Sequence, Golden Ratio - Mathematics Stack Exchange
8 May 2025 at 8:41am
Fibonacci sequence in the factorization of certain polynomials having a root at the Golden Ratio 4 What is the connection and the difference between the Golden Ratio and Fibonacci Sequence?
Is the Fibonacci sequence exponential? - Mathematics Stack Exchange
5 May 2025 at 4:16pm
So the fibonacci sequence, one item at a time, grows more slowly than $2^n$. But on the other hand every 2 items the Fibonacci sequence more than doubles itself: $(1) F_n = F_{n-1} + F_{n-2}$
What is the meaning of limit of Fibonacci sequence?
8 May 2025 at 12:09pm
The existence of the limit reflects the fact that the Fibonacci sequence is essentially a geometric sequence (it is actually a linear combination of two geometric sequences but one of them dominates the other). See Wikipedia.
Relationship between Primes and Fibonacci Sequence
25 Apr 2025 at 9:14pm
I recently stumbled across an unexpected relationship between the prime numbers and the Fibonacci sequence. We know a lot about Fibonacci numbers but relatively little about primes, so this connection seems worth exploring.
Inverse Fibonacci sequence - Mathematics Stack Exchange
8 May 2025 at 8:12am
I was having fun with Fibonacci numbers, and I had the idea to consider the sequence $ F_n=F_{n-1}^{-1}+F_{n-2}^{-1} $ instead. I wrote a simple program to compute the first terms and the sequence ...
Proof that Fibonacci Sequence modulo m is periodic? [duplicate]
6 May 2025 at 4:04am
Let us list out the Fibonacci sequence modulo m, where m is some integer. It will look something like this at first (for $10$ at least): $$ 1,2, 3,5,8, 3,1, 4, 5, 9, 4, 3, 7 {\dots}$$
combinatorics - Applications of the Fibonacci sequence - Mathematics ...
4 May 2025 at 10:36pm
This is precisely the recurrence relation of the Fibonacci numbers. Checking our base cases, we see that there is one way to tile a 1 x 2 grid and two ways to tile a 2 x 2 grid, so S 1 = 1 and S 2 = 2. Therefore, the number of tilings is precisely the Fibonacci sequence.
numerical methods - Fibonacci Sequence: Rate of Convergence ...
6 May 2025 at 3:28am
By computer the ratio of successive terms in the Fibonacci seqence shows a linear convergence, i.e., $\mu \in [0,1]$, of $1/\varphi^2 \approx .382$. Can anyone show this analytically? numerical-methods
recurrence relations - Fibonacci, tribonacci and other similar ...
5 May 2025 at 9:42am
I know the sequence called the Fibonacci sequence; it's defined like: $\begin{align*} F_0&=0\\ F_1&=1\\ F_2&=F_0+F_1\\ &\vdots\\ Fn&=F_{n-1} + F_{n-2}\end{align*}$
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
8 May 2025 at 2:22am
Fibonacci sequence, strings without 00, and binomial coefficient sums. 1. Proof of the relationship ...
Fibonacci Sequence, Golden Ratio - Mathematics Stack Exchange
8 May 2025 at 8:41am
Fibonacci sequence in the factorization of certain polynomials having a root at the Golden Ratio 4 What is the connection and the difference between the Golden Ratio and Fibonacci Sequence?
Is the Fibonacci sequence exponential? - Mathematics Stack Exchange
5 May 2025 at 4:16pm
So the fibonacci sequence, one item at a time, grows more slowly than $2^n$. But on the other hand every 2 items the Fibonacci sequence more than doubles itself: $(1) F_n = F_{n-1} + F_{n-2}$
What is the meaning of limit of Fibonacci sequence?
8 May 2025 at 12:09pm
The existence of the limit reflects the fact that the Fibonacci sequence is essentially a geometric sequence (it is actually a linear combination of two geometric sequences but one of them dominates the other). See Wikipedia.
Relationship between Primes and Fibonacci Sequence
25 Apr 2025 at 9:14pm
I recently stumbled across an unexpected relationship between the prime numbers and the Fibonacci sequence. We know a lot about Fibonacci numbers but relatively little about primes, so this connection seems worth exploring.
Inverse Fibonacci sequence - Mathematics Stack Exchange
8 May 2025 at 8:12am
I was having fun with Fibonacci numbers, and I had the idea to consider the sequence $ F_n=F_{n-1}^{-1}+F_{n-2}^{-1} $ instead. I wrote a simple program to compute the first terms and the sequence ...
Proof that Fibonacci Sequence modulo m is periodic? [duplicate]
6 May 2025 at 4:04am
Let us list out the Fibonacci sequence modulo m, where m is some integer. It will look something like this at first (for $10$ at least): $$ 1,2, 3,5,8, 3,1, 4, 5, 9, 4, 3, 7 {\dots}$$
combinatorics - Applications of the Fibonacci sequence - Mathematics ...
4 May 2025 at 10:36pm
This is precisely the recurrence relation of the Fibonacci numbers. Checking our base cases, we see that there is one way to tile a 1 x 2 grid and two ways to tile a 2 x 2 grid, so S 1 = 1 and S 2 = 2. Therefore, the number of tilings is precisely the Fibonacci sequence.
numerical methods - Fibonacci Sequence: Rate of Convergence ...
6 May 2025 at 3:28am
By computer the ratio of successive terms in the Fibonacci seqence shows a linear convergence, i.e., $\mu \in [0,1]$, of $1/\varphi^2 \approx .382$. Can anyone show this analytically? numerical-methods
recurrence relations - Fibonacci, tribonacci and other similar ...
5 May 2025 at 9:42am
I know the sequence called the Fibonacci sequence; it's defined like: $\begin{align*} F_0&=0\\ F_1&=1\\ F_2&=F_0+F_1\\ &\vdots\\ Fn&=F_{n-1} + F_{n-2}\end{align*}$
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
