A Factorial Sum Produces the Factorial Number System (visual proof)

This is a short, animated visual proof demonstrating a finite sum involving products of factorials. The proof exploits the classic inductive proof of the formula in question. As a bonus, we discuss the factorial number system and show how the formula can be used to count up in this system.
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This animation is based on a proofs by Tom Edgar from the December 2016 issue of Mathematics Magazine page 338 (doi.org/10.416....
If you want to know more about the factorial number system, check out en.wikipedia.o...
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