Question

$\lim_{n\to \infty}\frac{F_{n+1}^{k}}{F_{n}^{k}}=\lim_{n\to \infty}\frac{F_{n+k}}{F_n}=\phi^{k},$ true? for odd $k$'s?

score 72 · Answer 1 · 2026-03-26 01:12:37

72

Views

$\lim_{n\to \infty}\frac{F_{n+1}^{k}}{F_{n}^{k}}=\lim_{n\to \infty}\frac{F_{n+k}}{F_n}=\phi^{k},$ true? for odd $k$'s?

Published on 26 Mar 2026 - 1:12

score 82 · Answer 2 · 2023-05-14 10:47:55

82

Views

Golden number, diagonals of polygons and continued fractions

Published on 14 May 2023 - 10:47

score 55 · Answer 3 · 2023-05-16 11:41:46

55

Views

Limit of a series of a side of the Golden Ratio

Published on 16 May 2023 - 11:41

score 133 · Answer 4 · 2023-05-16 17:15:18

133

Views

Solving for $x$ in $x^5+x^4+x^3+x^2+x+1=0$

Published on 16 May 2023 - 17:15

score 484 · Answer 5 · 2026-03-23 00:57:49

484

Views

Self-made Sangaku-style geometry problem involving chords and inscribed circles

Published on 23 Mar 2026 - 0:57

score 69 · Answer 6 · 2023-06-01 12:59:49

69

Views

How to construct (with straightedge and compass) this diagram with four circles and two chords?

Published on 01 Jun 2023 - 12:59

score 90 · Answer 7 · 2023-06-03 09:07:27

90

Views

Nested radicals $\sqrt{C+1+b\sqrt{C+1+b^{2}\sqrt{C+1+b^{3}\sqrt{\cdot\cdot\cdot}}}}=g(x)$ then $\lim_{x\to\infty}(g(x+1)-g(x))=^?1$

Published on 03 Jun 2023 - 9:07

score 113 · Answer 8 · 2023-06-18 20:49:14

113

Views

Proof that the sequence $x_n=f_{n+1}/f_n$ convergences to the golden ration $\Phi$

Published on 18 Jun 2023 - 20:49

score 595 · Answer 9 · 2023-06-19 07:00:31

595

Views

What are the known methods of drawing a golden rectangle with a ruler and compass?

Published on 19 Jun 2023 - 7:00

score 1.9k · Answer 10 · 2023-06-19 10:19:43

1.9k

Views

The golden ratio in a parabola

Published on 19 Jun 2023 - 10:19

score 388 · Answer 11 · 2023-06-24 18:07:27

388

Views

Any cool ways to solve $\int_{0}^{\frac{\pi}{2}}\log(1+4\sin^2x)\,dx$

Published on 24 Jun 2023 - 18:07

score 293 · Answer 12 · 2023-07-02 07:09:38

293

Views

How to solve $\sin\left(1+\frac{1+\sqrt{5}}{2}\right)<1/2$?

Published on 02 Jul 2023 - 7:09

score 82 · Answer 13 · 2023-07-02 13:59:58

82

Views

Mixing Continued fraction and nested radicals does $D=-\pi+\ln(16)+(7\ln\pi)/2-7/3\arctan(\pi)$?

Published on 02 Jul 2023 - 13:59

score 82 · Answer 14 · 2023-07-05 12:03:52

82

Views

Which $x \in \mathbb R$ satisfy a property related to sequences

Published on 05 Jul 2023 - 12:03

score 64 · Answer 15 · 2023-07-09 14:51:49

64

Views

Is my reasoning using limits correct for why =1+1/?

Published on 09 Jul 2023 - 14:51

List Question

$\lim_{n\to \infty}\frac{F_{n+1}^{k}}{F_{n}^{k}}=\lim_{n\to \infty}\frac{F_{n+k}}{F_n}=\phi^{k},$ true? for odd $k$'s?

Golden number, diagonals of polygons and continued fractions

Limit of a series of a side of the Golden Ratio

Solving for $x$ in $x^5+x^4+x^3+x^2+x+1=0$

Self-made Sangaku-style geometry problem involving chords and inscribed circles

How to construct (with straightedge and compass) this diagram with four circles and two chords?

Nested radicals $\sqrt{C+1+b\sqrt{C+1+b^{2}\sqrt{C+1+b^{3}\sqrt{\cdot\cdot\cdot}}}}=g(x)$ then $\lim_{x\to\infty}(g(x+1)-g(x))=^?1$

Proof that the sequence $x_n=f_{n+1}/f_n$ convergences to the golden ration $\Phi$

What are the known methods of drawing a golden rectangle with a ruler and compass?

The golden ratio in a parabola

Any cool ways to solve $\int_{0}^{\frac{\pi}{2}}\log(1+4\sin^2x)\,dx$

How to solve $\sin\left(1+\frac{1+\sqrt{5}}{2}\right)<1/2$?

Mixing Continued fraction and nested radicals does $D=-\pi+\ln(16)+(7\ln\pi)/2-7/3\arctan(\pi)$?

Which $x \in \mathbb R$ satisfy a property related to sequences

Is my reasoning using limits correct for why =1+1/?

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