perplexus.info :: Just Math : The golden ratio

The golden ratio (Posted on 2015-09-16)

In a Fibonacci sequence 1, 1, 2, 3, 5, …, F_n, F_n+1
define R_n = F_n/ F_n-1

Prove that lim (R_n) as n approaches infinity
is .5*(1+sqrt(5))=1.618...
a.k.a. the golden ratio, φ (phi).

See The Solution Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: No Subject

Comment 6 of 6 |

(In reply to No Subject by JayDeeKay)

That works.

One small typo, JDK, that you might want to fix for posterity.

Euler-Binet formula, F(n) = (a^n - b^n ) / sqr(5)

Posted by Steve Herman on 2015-09-18 17:26:19

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info