Factorial Fractions

1 × 2 × 3 × ... × n = n!

(You probably know this already.)but,

1 ÷ 2 ÷ 3 ÷ ... ÷ n = 1/n!

Example:

1 ÷ 2 ÷ 3 ÷ 4 ÷ 5 = 1/120 = 1/5!

It doesn't matter what integer n is! But remember, division is NOT commutative!

5 ÷ 4 ÷ 3 ÷ 2 ÷ 1 = 5/24

which is not equal to

1/5!

Psst! Here's a tip! n^(-1) = 1/n, so 1 ÷ 2 ÷ 3 ÷ ... ÷ n = n!^(-1) It's the same thing!

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© Derek Cumberbatch