Why $\frac{F_{n+2}}{F_{n+1}}=1+\frac{F_n}{F_{n+1}}$ (seems to) hold for every fibonacci number $F_n$?
Asked
Active
Viewed 56 times
0
-
9Because $F_{n+2}=F_{n+1}+F_n$ – Hagen von Eitzen Nov 10 '18 at 17:35
-
1Multiply either side by $F_{n+1}$ to get the property of the series. – Narasimham Nov 11 '18 at 05:57
1 Answers
4
We know from the definition of the Fibonacci sequence that $F_{n+2}=F_{n+1}+F_{n}$.
Suppose that $n$ is such that $F_{n+1}\neq 0$.
Dividing both sides of the recursive formula given in the definition by $F_{n+1}$ yields the result.
JMoravitz
- 79,518