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lfdahl
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We have an $n \times n$ square grid of dots ($n \ge 2$).
Let $s_n$ denote the number of squares that can be constructed from the grid points.
(a). Show, that $$s_n = \frac{n^4-n^2}{12}.$$
Note, that squares with "diagonal sides" also count.
(b). Evaluate the sum:
\[S = \sum_{k = 2}^{\infty }\frac{1}{s_k}\]
Let $s_n$ denote the number of squares that can be constructed from the grid points.
(a). Show, that $$s_n = \frac{n^4-n^2}{12}.$$
Note, that squares with "diagonal sides" also count.
(b). Evaluate the sum:
\[S = \sum_{k = 2}^{\infty }\frac{1}{s_k}\]
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