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Math Help - Fibonacci

  1. #1
    Member javax's Avatar
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    Fibonacci

    Hello everybody. I need some help onn the problems. I always had problem with these:

    i). Prove that the n-th term of Fibonacci numbers is given with this formula:
    f_n=\frac{1}{\sqrt 5}\left(\left(\frac{1+\sqrt 5}{2}\right)^{n}-\left(\frac{1-\sqrt 5}{2}\right)^{n}\right)

    ii). Let it be F_n=2^{2^{n}}+1. Prove that F_0 F_1 F_2 \cdots F_{n-1}=F_n - 2, n>0

    I appreciate your help.
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  2. #2
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    Quote Originally Posted by javax View Post
    Hello everybody. I need some help onn the problems. I always had problem with these:

    i). Prove that the n-th term of Fibonacci numbers is given with this formula:
    f_n=\frac{1}{\sqrt 5}\left(\left(\frac{1+\sqrt 5}{2}\right)^{n}-\left(\frac{1-\sqrt 5}{2}\right)^{n}\right)

    ii). Let it be F_n=2^{2^{n}}+1. Prove that F_0 F_1 F_2 \cdots F_{n-1}=F_n - 2, n>0

    I appreciate your help.
    Please see

    Fibonacci number - Wikipedia, the free encyclopedia
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