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  "body": "\n## Statement\n\nLet $n$ be a positive integer. Then the $n$ smallest odd positive integers add up to the square of $n$:\n$$1 + 3 + 5 + \\dots + (2n - 1) = \\sum_{i=1}^{n} (2i - 1) = n^2.$$\n\n## Remarks\n\nFor $n = 1, 2, 3, 4$ the sums are $1, 4, 9, 16$.\nA proof by [[induction|0ASJVEFA9J]] uses $n^2 + (2n + 1) = (n + 1)^2$.\n",
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