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Thread: Combinatorial proof help

  1. September 30th 2009, 05:43 PM #1
    absvalue
    absvalue is offline
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    Combinatorial proof help

    I'm lost. Could someone explain to me how I would approach these problems?

    1a) Prove this equation combinatorially
    2 \times 3^0 + 2 \times 3^1 + 2 \times 3^2 + ... + 2 * 3^{n-1} = 3^n - 1

    Next, solve this equation using ordinary base-10 numbers:
    2 \times 10^0 + 2 \times 10^1 + 2 \times 10^2 + ... + 2 * 10^{n-1} = 10^n - 1

    1b) Let a and b be positive integers with a > b. Give a combinatorial proof of the identity (a + b)(a - b) = a^2 - b^2.
    Last edited by absvalue; September 30th 2009 at 08:56 PM.
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