Odd numbers make squares
Visual
1 + 3 + 5 + \cdots + (2n-1) = n^2. Picture an n \times n grid of dots and peel it into L-shaped layers from one corner: the layers have 1, 3, 5, \dots dots. No induction required.
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Antony
November 2, 2026
1 + 3 + 5 + \cdots + (2n-1) = n^2. Picture an n \times n grid of dots and peel it into L-shaped layers from one corner: the layers have 1, 3, 5, \dots dots. No induction required.