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