Thomas Morrill

Proof Without Words: Arithmetic Progressions

The YouTube channel Mathologer posted a wonderful demonstration of a classical result,

1 + 2 = 3
4 + 5 + 6 = 7 + 8
9 + 10 + 11 + 12 = 13 +14 +15
\vdots

I thought I would give my own twist on it:

\sum_{k=0}^n (n^2 + k) = \sum_{k=n+1}^{2n} (n^2 + k)

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