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Math Help - [SOLVED] Fibonacci

  1. #1
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    [SOLVED] Fibonacci

    Let a be the 1000th Fibonacci number; and,

    Let b be the 1001st Fibonacci number.

    Then, write the 1003rd Fib. number in terms of a and b. Simplify.

    ---

    So F_{1000} = a, F_{1001} = b, then

    a + b = F_{1002} = c

    And so c+b = F_{1003}

    I doubt this is right because I'm introducing a new constant. Any ideas?
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  2. #2
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    Quote Originally Posted by Startbucks View Post
    I doubt this is right because I'm introducing a new constant. Any ideas?
    Yes, but what is c? Just a+b, so you can substitute them back in.

    Here is how I would write it:

    a=F_{1000},\,b=F_{1001}

    so

    F_{1003}=F_{1001}+F_{1002}=b+F_{1002}

    =b+(F_{1000}+F_{1001})=b+(a+b)=a+2b\text.

    Edit: I saw that, Moo Too slow, but you could have left it.
    Last edited by Reckoner; February 24th 2009 at 09:34 AM.
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