Question

Proving $\sum_{j=0}^n (-1)^j {n \choose j} F_{s+2n-2j} = F_{s+n} $, where $F_n$ is the $n$-th Fibonacci number

score 134 · Answer 1 · 2018-08-01 04:09:14

134

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Proving $\sum_{j=0}^n (-1)^j {n \choose j} F_{s+2n-2j} = F_{s+n} $, where $F_n$ is the $n$-th Fibonacci number

Published on 01 Aug 2018 - 4:09

score 890 · Answer 2 · 2026-03-17 23:14:41

890

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Derivation of Fibonacci sequence by difference equation/Z transform

Published on 17 Mar 2026 - 23:14

score 200 · Answer 3 · 2018-08-10 05:20:39

200

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Does my rearrangement of the sequence to prove that - any $n\in\mathbb N$ can be written as the sum of Fibonacci numbers - look fine?

Published on 10 Aug 2018 - 5:20

score 91 · Answer 4 · 2018-08-10 22:48:55

91

Views

Write $F_{1}-F_{2}+F_{3}-F_{4}+...+F_{2n-1}-F_{2n}$ as a summation

Published on 10 Aug 2018 - 22:48

score 62 · Answer 5 · 2026-03-25 03:03:45

62

Views

Proving that $\left | \frac{1+\sqrt{5}}{2}-R_k \right |>\frac{1}{Q_k^2\sqrt{5}}$.

Published on 25 Mar 2026 - 3:03

score 137 · Answer 6 · 2026-03-25 02:58:51

137

Views

Fibonacci sieve and factoring

Published on 25 Mar 2026 - 2:58

score 207 · Answer 7 · 2026-03-25 04:44:21

207

Views

Ratio of 0's to 1's in the Fibonacci Word is the golden ratio

Published on 25 Mar 2026 - 4:44

score 117 · Answer 8 · 2018-08-23 02:06:21

117

Views

Constant-recursive Fibonacci identities

Published on 23 Aug 2018 - 2:06

score 1k · Answer 9 · 2018-08-28 23:12:26

1k

Views

Showing that the $n$-th Fibonacci number $f_n$ satisfies $f_n < 2^n$

Published on 28 Aug 2018 - 23:12

score 92 · Answer 10 · 2018-08-29 23:27:07

92

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Evaluating $\sum\limits_{n \ge 0} \frac{1}{x^{2^n}-y^{2^n}}$ where $x, y \in \mathbb R^{+}$ and $x \ne y, x>1.$

Published on 29 Aug 2018 - 23:27

score 335 · Answer 11 · 2018-08-30 03:58:27

335

Views

Fibonacci Coding Inductive Proof

Published on 30 Aug 2018 - 3:58

score 1.6k · Answer 12 · 2026-03-25 04:37:56

1.6k

Views

Continued fraction involving Fibonacci sequence

Published on 25 Mar 2026 - 4:37

score 130 · Answer 13 · 2018-09-04 12:09:01

130

Views

Fibonaccith fibonacci number

Published on 04 Sep 2018 - 12:09

score 339 · Answer 14 · 2018-09-10 19:10:50

339

Views

Fibonacci summation proof using matrices?

Published on 10 Sep 2018 - 19:10

score 318 · Answer 15 · 2026-03-22 23:07:45

318

Views

How to construct spiral phyllotactic pattern with the given number of spirals?

Published on 22 Mar 2026 - 23:07

List Question

Proving $\sum_{j=0}^n (-1)^j {n \choose j} F_{s+2n-2j} = F_{s+n} $, where $F_n$ is the $n$-th Fibonacci number

Derivation of Fibonacci sequence by difference equation/Z transform

Does my rearrangement of the sequence to prove that - any $n\in\mathbb N$ can be written as the sum of Fibonacci numbers - look fine?

Write $F_{1}-F_{2}+F_{3}-F_{4}+...+F_{2n-1}-F_{2n}$ as a summation

Proving that $\left | \frac{1+\sqrt{5}}{2}-R_k \right |>\frac{1}{Q_k^2\sqrt{5}}$.

Fibonacci sieve and factoring

Ratio of 0's to 1's in the Fibonacci Word is the golden ratio

Constant-recursive Fibonacci identities

Showing that the $n$-th Fibonacci number $f_n$ satisfies $f_n < 2^n$

Evaluating $\sum\limits_{n \ge 0} \frac{1}{x^{2^n}-y^{2^n}}$ where $x, y \in \mathbb R^{+}$ and $x \ne y, x>1.$

Fibonacci Coding Inductive Proof

Continued fraction involving Fibonacci sequence

Fibonaccith fibonacci number

Fibonacci summation proof using matrices?

How to construct spiral phyllotactic pattern with the given number of spirals?

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