# Combinatorial proof help

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• September 30th 2009, 05:43 PM
absvalue
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 $(a + b)(a - b) = a^2 - b^2$.