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Math Help - help with Lucas numbers

  1. #1
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    help with Lucas numbers

    Given L_{1}=1,L_{2}=3,L_{n+2}=L_{n}+L_{n+1}, how can I prove that L_{3}=\alpha^3-\alpha^{-3} where \alpha=\frac{1+\sqrt{5}}{2}??
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  2. #2
    Senior Member Shanks's Avatar
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    If you are supposed to find L_3, then just check if the equality hold or not.
    If you are supposed to find the formulla of L_n, the characteristic equation x^2-x-1=0(can you find the roots)will help you.
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