- #1
moo5003
- 207
- 0
Basically my problem comes down to an algebra thing. This is a proofs class and I'm trying to show using strong induction that the fionacci numbers to the nth power can be given by the formula
1 / Radical (5) [ (1+Rad(5) / 2) ^ n - (1-Rad(5) / 2) ^ n.
My problem comes down to the induction step.. after substiting the assumed for f(n) and f(n-1) and adding those to equal f(n+1) I have no clue how to get the equation given by f(n) + f(n-1) represent the above witn n+1 as the powers instead of n. Any help here would be greatly appreciated.
1 / Radical (5) [ (1+Rad(5) / 2) ^ n - (1-Rad(5) / 2) ^ n.
My problem comes down to the induction step.. after substiting the assumed for f(n) and f(n-1) and adding those to equal f(n+1) I have no clue how to get the equation given by f(n) + f(n-1) represent the above witn n+1 as the powers instead of n. Any help here would be greatly appreciated.