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Math Help - inductive math (I'm missing something)

  1. #1
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    inductive math (I'm missing something)

    fn is the nth Fibonacci number

    Prove that f1(^2)+f2(^2)+...+fn(^2)=fn fn+1 whenever n is a positive integer.

    Here's what I have so far:

    Let P(n) be f1(^2)+f2(^2)+...fn(^2)=fn fn+1

    Basis step: P(1) is true since f1(2)=1=f2(^2)

    Inductive Step: Assume P(n)) is true
    Then f1(^2)+f2(^2)+...fn(^2)+fn+1(^2)=fn fn+1 + fn+1(^2)


    Have I done this right so far, and if so, where do I go from here?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sjenkins View Post
    fn is the nth Fibonacci number

    Prove that f1(^2)+f2(^2)+...+fn(^2)=fn fn+1 whenever n is a positive integer.

    Here's what I have so far:

    Let P(n) be f1(^2)+f2(^2)+...fn(^2)=fn fn+1

    Basis step: P(1) is true since f1(2)=1=f2(^2)
    this is wrong. you haven't verified the statement holds for the base case

    Inductive Step: Assume P(n)) is true
    Then f1(^2)+f2(^2)+...fn(^2)+fn+1(^2)=fn fn+1 + fn+1(^2)


    Have I done this right so far, and if so, where do I go from here?
    Hint: f_{n + 1} = f_{n - 1} + f_n

    (and in general, you get the next Fibonacci number by adding the previous two, this will come in handy)
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