MisterPants
Senior member
In the fibonacci sequence:
1) t10/t11 = t10/(t9+t10).
2) 1/(1+(t10/t11))=(t11/t12).
Both of these apply to any terms n+1 and n.
3) As n approaches infinity, lim tn/t(n+1) = (5^(1/2) - 1)/2.
Can anybody show that part 3 follows from 1 and 2 or any other properties of the sequence?
1) t10/t11 = t10/(t9+t10).
2) 1/(1+(t10/t11))=(t11/t12).
Both of these apply to any terms n+1 and n.
3) As n approaches infinity, lim tn/t(n+1) = (5^(1/2) - 1)/2.
Can anybody show that part 3 follows from 1 and 2 or any other properties of the sequence?
