What do Fibonacci numbers, 1,1,2,3,5, etc. have to do with the golden ratio, 1.618??? What's the relationship?

The ratio of the numbers approach the golden ratio
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615+
34/21 = 1.619+ etc/

The relationships are:
1. As n increases F(n+1)/F(n) approaches ϕ
2. F(n) = (ϕⁿ - (-ϕ)⁻ⁿ) / √5
3. ϕⁿ = F(n)ϕ + F(n-1)
Starting from F(0)=0 and F(1)=1, and where ϕ is the Golden Ratio, with the value (1+√5)/2

The ratio of the any number, n in this sequence to its prior number tends to be the Golden ratio as n tends to infinity.

The ratio of the numbers approach the golden ratio
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615+
34/21 = 1.619+ etc/

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