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OK! Now Prove It
Age 16 to 18
Challenge Level 
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.
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