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Math Help - Trees

  1. #1
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    Proof

    Prove the following by induction on n

    1+5+9+....+(4n-3) = n(2n-1) for all n => 1
    Last edited by Tom101; April 20th 2008 at 05:25 AM. Reason: wrong questions
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Tom101 View Post
    Prove the following by induction on n

    1+5+9+....+(4n-3) = n(2n-1) for all n => 1

    check base case n=1

    1=1(2(1)-1) true

    assume n=k

    1+5+9+....+(4k-3)=k(2k-1)

    Show k+1

    1+5+9+....+(4k-3)+[4(k+1)-3]=
    by the induction hypothsis
    k(2k-1)+[4(k+1)-3]=2k^2-k+4k+4-3=2k^2+3k+1=

    (k+1)(2k+1)=(k+1)(2(k+1)-1)

    The last one is k+1

    QED
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