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Notice that $$1^2 = {1\times 2\times 3 \over 6}$$ $$1^2 + 3^2 = {3\times 4\times 5 \over 6}$$ $$1^2 + 3^2 + 5^2 = {5\times 6\times 7 \over 6}.$$ Make a conjecture about the sum $$1^2 + 3^2 + 5^2 + \dots + (2n - 1)^2$$ and prove your conjecture.