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Fibonacci sequence

  1. Aug 30, 2008 #1
    if [tex]a_1, a_2, a_3 .............[/tex] belong to the fibonacci sequence, prove that

    [tex]a_1a_2 + a_2a_3 + ............ + a_{2n-1}a_{2n} = (a_{2n})^2[/tex]
  2. jcsd
  3. Aug 30, 2008 #2


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    If you are familiar with mathematical induction then that's the way to go with this one. Using the recursion equation ([itex]a_{2n} + a_{2n+1} = a_{2n+2}[/itex] etc) should let you make the inductive step fairly easily.

    BTW. Is this homework ?
  4. Aug 30, 2008 #3
    not at all!!!
  5. Aug 30, 2008 #4


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    Are you familar with mathematical induction?
  6. Aug 30, 2008 #5
    Is there any other method other than this?
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