List questions from fibonacci-numbers

Published on 16 Apr 2026 - 22:18

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Compute $\sum\limits_{n=1}^\infty \arctan\left(\frac{(-1)^{n+1}}{F_{n+1}(F_n+F_{n+2})}\right)$, where $F_n$ is $n$th Fibonacci number

Published on 16 Apr 2026 - 11:12

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Powers of the golden ratio

Published on 10 May 2026 - 12:42

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Values of Fibonacci polynomials

Published on 15 Apr 2026 - 12:48

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Consecutive Fibonacci Numbers

Published on 09 Apr 2026 - 19:49

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Factoring Fibonacci polynomials

Published on 13 Apr 2026 - 19:07

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Variable transformation $x\to x+1$ in Fibonacci-polynomial $F_n(x)$

Published on 16 Apr 2026 - 21:26

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Fibonacci numbers and perfect squares

Published on 10 May 2026 - 12:40

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Why is $x$ always a perfect square?

Published on 10 May 2026 - 12:40

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Fibonacci sequences as a vector space

Published on 15 Apr 2026 - 23:18

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Given a fibonacci sequence where $f(n)=f(n-1)+f(n-2) for \space n\ge 2 $and $f(0)=0,f(1)=1$

Published on 17 Apr 2026 - 3:02

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An inequality problem with Fibonacci numbers - From a pdf called Fibonacci numbers and 2018

Published on 09 Apr 2026 - 6:24

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Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number

Published on 25 Mar 2026 - 6:06

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Number of prime factors of the product of the first Fibonacci numbers

Published on 13 Apr 2026 - 21:08

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Proof of winning strategy in Fibonacci Nim

Published on 10 Apr 2026 - 5:27

List Question

If $F_n$ is the Fibonacci sequence, show that $F_n < \left(\frac 74\right)^n$ for $n\geq 1.$

Compute $\sum\limits_{n=1}^\infty \arctan\left(\frac{(-1)^{n+1}}{F_{n+1}(F_n+F_{n+2})}\right)$, where $F_n$ is $n$th Fibonacci number

Powers of the golden ratio

Values of Fibonacci polynomials

Consecutive Fibonacci Numbers

Factoring Fibonacci polynomials

Variable transformation $x\to x+1$ in Fibonacci-polynomial $F_n(x)$

Fibonacci numbers and perfect squares

Why is $x$ always a perfect square?

Fibonacci sequences as a vector space

Given a fibonacci sequence where $f(n)=f(n-1)+f(n-2) for \space n\ge 2 $and $f(0)=0,f(1)=1$

An inequality problem with Fibonacci numbers - From a pdf called Fibonacci numbers and 2018

Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number

Number of prime factors of the product of the first Fibonacci numbers

Proof of winning strategy in Fibonacci Nim

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