1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fibonacci Number Crunch

  1. Mar 28, 2006 #1
    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.
     
  2. jcsd
  3. Mar 28, 2006 #2

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    Hint:

    [tex]\frac{1\pm\sqrt{5}}{2}[/tex]

    are the solutions to x² - x - 1 = 0, so they satisfy x+1 = x². Anyways, please use LaTeX and show your work, because this problem is quite straightforward, so it's hard to guess where you're getting stuck. Therefore, it's hard to know what hint to give that will be useful but won't give too much away.
     
    Last edited: Mar 28, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fibonacci Number Crunch
  1. Fibonacci Numbers (Replies: 7)

  2. Fibonacci Numbers (Replies: 1)

  3. Fibonacci Numbers (Replies: 0)

  4. Fibonacci numbers (Replies: 1)

Loading...