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what is the formula for finding the number of squares on any sized chessboard, whether...
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High School Teacher
2x2: 1 + 2*2
3x3: 1 + 2*2 + 3*3
4x4: 1 + 2*2 + 3*3 + 4*4
I think I see the pattern, but we need a formula. Imagine each square number as a physical square (made out of wood or something, like a collection of chessboards), and you stack them up, forming a pyramid. Volume of a pyramid is `1/3Bh`, so we should see `1/3n^3` in our answer.
In fact, the sum of the first n square numbers is `(2n^3+3n^2+n)/6` , which is the formula you were after.
Posted by nathanshields on January 12, 2012 at 8:06 AM (Answer #1)
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