Question

what is golden ratio?How we relate it with Fibonacci series?

Answer 1

actually golden ratio is 1 : 1.618.

the Fibonacci series is
1,1,2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

So, dividing each number by the previous number gives: 1 / 1 = 1, 2 / 1 = 2, 3 / 2 = 1.5, and so on up to 144 / 89 = 1.6179…. The resulting sequence is:

1, 2, 1.5, 1.666..., 1.6, 1.625, 1.615…, 1.619…, 1.6176…, 1.6181…, 1.6179…

But do you notice anything about those numbers? Perhaps the fact that they keep oscillating around and getting tantalizingly closer and closer to 1.618?—the value of phi: the golden ratio! Indeed, completely unbeknownst to Fibonacci, his solution to the rabbit population growth problem has a deep underlying connection to the golden ratio.