I was explaining to a co-worker how supposed worked out the formula and illustrating my simple proof. I tried to look it up online, but didn’t find it.

So, here it is:

1 | 2 | … | N | = |

N | N-1 | … | 1 | = |

N+1 | N+1 | … | N+1 | = |

Thus

For a better explanation, see this PDF.

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