1. Limited time only! Sign up for a free 30min personal 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!

How to proof; a sumformula

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Proof that [tex]\sum a, m=0, [/tex] (a-m)! / m!(a-2m)! = the fibonacci sequence.
    2. Relevant equations
    Fibonacci: 1, 1, 2, 3, 5, ... (but I think everyone knows that one!)
    3. The attempt at a solution
    Let Xm = [tex]\suma m=0[/tex] (a-m)! / m!(a-2m)!
    I think I better proof Xm+2 = Xm+1 + Xm (follows from the fibonacci), so I can conclude that Xm = Fm+1.
    I think using induction is the best way to go: Prooving it for X0 and X1, maybe even X2.
    My attempt:
    [tex]\sum a+2, m=0, [/tex] (a+2-m)! / m!(a+2-2m)! = [tex]\sum a+1, m=0, [/tex] (a+1-m)! / m!(a+1-2m)! + [tex]\sum a, m=0, [/tex] (a-m)! / m!(a-2m)!
    =[tex]\sum a+1, m=0, [/tex] (a+1-m)! / m!(a+1-2m)! + [tex]\sum a+1, m=1, [/tex] (a-m-1)! / (m-1)!(a-m-1-m+1)! ... but I think I am making big mistakes here, because whatever I do, I get stuck.
    I just don't see it!

    Vince, freshmen physics, sorry but I don't know how to use the symbols and stuff!
  2. jcsd
  3. Nov 15, 2009 #2
    It's difficult to read what you have written. Try editing it by using the proper LaTeX. Just click on my output below to see the way to do it.
    [tex]\sum_{n=0}^\infty a_n[/tex] for sums and subscripts
    [tex]\frac{(a-m)!}{m!(a-2m)!}[/tex] for fractions
    Also, what is Xm?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: How to proof; a sumformula
  1. How to proof 0\0=? (Replies: 24)

  2. How to proof RHOMB (Replies: 3)