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Math Help - Induction for sequences

  1. #1
    Junior Member
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    Induction for sequences


    OK, I am completely stupid when it comes to induction. Any help? I shouldn't have taken this class.
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  2. #2
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
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    Use Mathematicla induction for part 1.
    let S_n be a statement that a_n is odd

    Assume S_{k-2} and S_{k-1} are true and then prove S_k is true.

    a_k = 2a_{k-2} +3a_{k-1}

    Now 2a_{k-2} is even and 3a_{k-1} is odd since odd multiplied by odd is odd.

    Sum of an even number and odd number is always odd.
    so a_k is odd.
    Hence S_k is proved true.

    base case a_1 and a_2 are already give odd.
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