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The solution to this problem was discovered by Gauss when he realized that if you write the numbers 1, 2, 3, ... down a column until you reach the midway point, and then start writing the remaining ones up the next column, that each row was the exact same sum.

The equation for the sum of the integers 1 to n is 1/2(n)(n+1).

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Q: What is a fast way to sum integers 1 to n?
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