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Proof by induction

  1. May 9, 2012 #1
    1. The problem statement, all variables and given/known data
    I have proved the first one and im trying to do the second using the result from part 1)


    2. Relevant equations

    [itex]F_1=1, F_2=2, F_n=F_{n-1}+F_{n-2}[/itex]

    3. The attempt at a solution
    base case: [itex]F_1|F_k[/itex] since[itex] F_1=1[/itex]

    Assume it works for n, [itex]F_n|F_{kn}[/itex]
    show [itex]F_{n+1}|F_{kn+k}[/itex]

    Well, using the part 1)
    [itex]F_{kn+k}=F_kF_{kn+1}+F_{k-1}F_{kn}[/itex]

    That's as far as i could go..
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

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  2. jcsd
  3. May 9, 2012 #2
    I have uplloaded the problem statement in the attachment
    sorry i forgot to mention that
     
    Last edited: May 9, 2012
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