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A Geometric Proof of the Square Pyramidal Number Formula

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side length n
5
spacing
opacity
The pyramidal numbers 1, 5, 14, 30, … are the sums of the square numbers,
P
n
=1+4+…+
2
n
. This Demonstration shows a geometric proof of the square pyramidal number formula,
P
n
=n(n+1)(2n+1)/6
. In the figure the six pyramids of side length
n
form an
n×(n+1)×(2n+1)
cuboid.
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