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).

Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

Solution: (Hide)

JayDeeKay's proof:
http://perplexus.info/show.php?pid=9927&cid=55703

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: No Subject	Steve Herman	2015-09-18 17:26:19
No Subject	JayDeeKay	2015-09-18 15:58:36
Discretion helps	Steve Herman	2015-09-18 12:56:14
re(2): Solution	Steve Herman	2015-09-18 07:37:32
re: Solution	Steve Herman	2015-09-16 12:28:30
Solution	JayDeeKay	2015-09-16 09:17:40

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