# 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:

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