Question

Proof $\sum_{k=0}^\infty \binom{k}{n-k} = f_{n+1}$ where $f_n$ is the n-th Fibonacci-number

score 335 · Answer 1 · 2019-01-24 21:13:14

335

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Proof $\sum_{k=0}^\infty \binom{k}{n-k} = f_{n+1}$ where $f_n$ is the n-th Fibonacci-number

Published on 24 Jan 2019 - 21:13

score 296 · Answer 2 · 2026-03-22 11:17:32

296

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Fibonacci primes vs Mersenne primes

Published on 22 Mar 2026 - 11:17

score 51 · Answer 3 · 2019-01-28 23:15:03

51

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Andrew wants to cross a 12-foot long bridge. He can either take a 1 foot step or a 2 foot step.Provide a recursive formula for this problem.

Published on 28 Jan 2019 - 23:15

score 150 · Answer 4 · 2019-01-30 12:38:03

150

Views

Show that $\begin{bmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{bmatrix} = \begin{bmatrix}1&1\\1&0\end{bmatrix}^n$ for all $n ∈ N$.

Published on 30 Jan 2019 - 12:38

score 392 · Answer 5 · 2019-02-04 22:26:30

392

Views

A sum of Fibonacci numbers

Published on 04 Feb 2019 - 22:26

score 61 · Answer 6 · 2019-02-04 22:51:11

61

Views

Question regarding the First Few Terms of a Fibonacci-like Recurrence.

Published on 04 Feb 2019 - 22:51

score 960 · Answer 7 · 2019-02-05 21:26:42

960

Views

Proving that every natural number can be expressed as the sum of distinct Fibonacci numbers

Published on 05 Feb 2019 - 21:26

score 440 · Answer 8 · 2019-02-06 02:27:25

440

Views

Counting 4-digit combinations such that the first digit is positive and even, second is prime, third is Fibonacci, and fourth is triangular

Published on 06 Feb 2019 - 2:27

score 58 · Answer 9 · 2019-02-06 19:53:38

58

Views

Storing numbers in an efficient way in computer.

Published on 06 Feb 2019 - 19:53

score 117 · Answer 10 · 2026-03-25 15:43:44

117

Views

What are $x$ and $y$ in $xF_n$ + $yF_{n-1}$ = $1$?

Published on 25 Mar 2026 - 15:43

score 57 · Answer 11 · 2026-03-26 06:31:11

57

Views

Fibonacci's sequence to calculate growth of a family

Published on 26 Mar 2026 - 6:31

score 69 · Answer 12 · 2019-02-16 20:05:21

69

Views

For $F(n)$ the $n$-th Fibonacci number, is $F(a)F(b)-F(a+1)F(b-1)$ always $\pm F(m)$ for some $m$?

Published on 16 Feb 2019 - 20:05

score 85 · Answer 13 · 2019-02-18 05:21:13

85

Views

Prove that \[(x^{2} +xy -y^{2})^{2}=1\] has consecutive Fibonacci numbers as solution

Published on 18 Feb 2019 - 5:21

score 203 · Answer 14 · 2026-03-25 17:21:36

203

Views

How can I use the relationship between the Fibonacci numbers and the EA to fill squares?

Published on 25 Mar 2026 - 17:21

score 92 · Answer 15 · 2019-02-25 13:09:00

92

Views

Proving that if $E_n$ is an even number of the Fibonacci sequence, then the next even number is $E_{n+1} = 4E_{n} + E_{n-1}$

Published on 25 Feb 2019 - 13:09

List Question

Proof $\sum_{k=0}^\infty \binom{k}{n-k} = f_{n+1}$ where $f_n$ is the n-th Fibonacci-number

Fibonacci primes vs Mersenne primes

Andrew wants to cross a 12-foot long bridge. He can either take a 1 foot step or a 2 foot step.Provide a recursive formula for this problem.

Show that $\begin{bmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{bmatrix} = \begin{bmatrix}1&1\\1&0\end{bmatrix}^n$ for all $n ∈ N$.

A sum of Fibonacci numbers

Question regarding the First Few Terms of a Fibonacci-like Recurrence.

Proving that every natural number can be expressed as the sum of distinct Fibonacci numbers

Counting 4-digit combinations such that the first digit is positive and even, second is prime, third is Fibonacci, and fourth is triangular

Storing numbers in an efficient way in computer.

What are $x$ and $y$ in $xF_n$ + $yF_{n-1}$ = $1$?

Fibonacci's sequence to calculate growth of a family

For $F(n)$ the $n$-th Fibonacci number, is $F(a)F(b)-F(a+1)F(b-1)$ always $\pm F(m)$ for some $m$?

Prove that \[(x^{2} +xy -y^{2})^{2}=1\] has consecutive Fibonacci numbers as solution

How can I use the relationship between the Fibonacci numbers and the EA to fill squares?

Proving that if $E_n$ is an even number of the Fibonacci sequence, then the next even number is $E_{n+1} = 4E_{n} + E_{n-1}$

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