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Math Help - Math Induction

  1. #1
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    Math Induction

    Use to math induction prove:
    F1^2 + F2^2 + + Fn^2 = FnFn+1







    Please help. Im stuck at the inductive step >.<
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by smoothi963 View Post
    Use to math induction prove:
    F1^2 + F2^2 + + Fn^2 = FnFn+1



    Please help. Im stuck at the inductive step >.<
    Not enough information. What is Fk?

    RonL
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  3. #3
    MHF Contributor

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    This is fairly standard in discrete mathematics courses for the Fibonacci sequence.
    Attached Files Attached Files
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Plato View Post
    This is fairly standard in discrete mathematics courses for the Fibonacci sequence.
    Yeah, i thought it had something to do with Fibonacci numbers
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  5. #5
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    Hello, smoothi963!

    We all assume that these are Fibonacci Numbers.


    Use induction to prove:

    . . (F
    1) + (F2) + (F3) + + (Fn) .= .(Fn)(Fn+1)

    I assume you've verified statement S(1) already.


    Assume statement S(k):

    . . (F
    1) + (F2) + (F3) + ... + (Fk) .= .(Fk)(Fk+1)


    Add (F
    k+1) to both sides:

    . . (F
    1) + (F2) + (F3) + ... + (Fk+1) .= .(Fk)(Fk+1) + (Fk+1)


    The LHS is the left side of S(k+1).


    Factor the right side: .F
    k+1(Fk + Fk+1) . = .(Fk+1)(Fk+2)
    . . . . . . . . . . . . . . . . . . . \_______/
    . . . . . . . . . . . . . . . . . . .
    this is Fk+2

    . . and we have the RHS of S(k+1).


    And the inductive proof is complete.

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  6. #6
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    Ahh thank you! Yes it is associated with the fibonnaci number, and sorry for not clarifying it. Thanks alot
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