Question

Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

score 342 · Answer 1 · 2014-10-24 01:26:11

342

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Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

Published on 24 Oct 2014 - 1:26

score 1.3k · Answer 2 · 2014-10-24 10:57:01

1.3k

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Find the sum of an infinite series of Fibonacci numbers divided by doubling numbers.

Published on 24 Oct 2014 - 10:57

score 3.4k · Answer 3 · 2014-10-27 02:52:47

3.4k

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Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

Published on 27 Oct 2014 - 2:52

score 272 · Answer 4 · 2014-10-27 21:34:42

272

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Does this sequence contain all positive integers?

Published on 27 Oct 2014 - 21:34

score 178 · Answer 5 · 2014-10-28 16:20:35

178

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geometric proof for fibonacci numbers identity with sum of two squares

Published on 28 Oct 2014 - 16:20

score 4.9k · Answer 6 · 2026-03-25 22:05:56

4.9k

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Show that Fibonacci and Lucas numbers satisfy the following equality for all n ≥ 2.

Published on 25 Mar 2026 - 22:05

score 370 · Answer 7 · 2014-10-28 22:21:34

370

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how to calculate a modified fibonacci via matrix exponentiation

Published on 28 Oct 2014 - 22:21

score 2.3k · Answer 8 · 2026-03-26 21:27:15

2.3k

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How many distinct ways to climb stairs in 1 or 2 steps at a time? (Fibonacci puzzle)

Published on 26 Mar 2026 - 21:27

score 631 · Answer 9 · 2026-03-25 14:06:24

631

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Mean and Variance of Fibonacci Numbers

Published on 25 Mar 2026 - 14:06

score 1.2k · Answer 10 · 2014-11-02 15:41:57

1.2k

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Fibonacci Number basis Induction

Published on 02 Nov 2014 - 15:41

score 69 · Answer 11 · 2014-11-03 00:45:26

69

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Proof of: $f_{n}^{2} = f_{n-1}f_{n+1}+(-1)^{n+1}$

Published on 03 Nov 2014 - 0:45

score 67 · Answer 12 · 2014-11-03 07:24:34

67

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Prove $f_{n}^{2} = f_{n-2}f_{n+2}+(-1)^{n}$ $n\ge 3$

Published on 03 Nov 2014 - 7:24

score 332 · Answer 13 · 2014-11-03 10:53:14

332

Views

How to show that the limit of a fibonacci sequence equates to 1 as n goes to infinity

Published on 03 Nov 2014 - 10:53

score 101 · Answer 14 · 2014-11-04 00:45:08

101

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Uniform Convergence for a sequence of functions defined by recurrence

Published on 04 Nov 2014 - 0:45

score 2.3k · Answer 15 · 2026-03-25 20:32:45

2.3k

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Understanding this pattern behind the Fibonacci sequence

Published on 25 Mar 2026 - 20:32

List Question

Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

Find the sum of an infinite series of Fibonacci numbers divided by doubling numbers.

Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

Does this sequence contain all positive integers?

geometric proof for fibonacci numbers identity with sum of two squares

Show that Fibonacci and Lucas numbers satisfy the following equality for all n ≥ 2.

how to calculate a modified fibonacci via matrix exponentiation

How many distinct ways to climb stairs in 1 or 2 steps at a time? (Fibonacci puzzle)

Mean and Variance of Fibonacci Numbers

Fibonacci Number basis Induction

Proof of: $f_{n}^{2} = f_{n-1}f_{n+1}+(-1)^{n+1}$

Prove $f_{n}^{2} = f_{n-2}f_{n+2}+(-1)^{n}$ $n\ge 3$

How to show that the limit of a fibonacci sequence equates to 1 as n goes to infinity

Uniform Convergence for a sequence of functions defined by recurrence

Understanding this pattern behind the Fibonacci sequence

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