Question

What is 1+ 1 over 1 + 1 over 1+1.....?

ie 1+ 1/1 = 2, 1+1/(1+1) =3/2, 5/3, etc..

Answer 1

Isn't that the golden ration definition ?

Answer 2

\[\Phi = \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + ...}}} = 1.618...\]

Answer 3

Don't be lazy, exact value please :-)

Answer 4

\[(1/2)(1+\sqrt{5})\]

Answer 5

The definition of the Golden ratio involves dividing a line segment in two parts, say a and b, so that (a+b)/a = a/b.

It is the positive root of x^2-x-1.

Answer 6

The sequence given in the question is the ratio of successive terms of the Fibonacci series.