Al Hazen's summation formulas, degree 1
The Arabic mathematical Al Hazen developed a method for adding all the powers of integers, here the first power:
The method involves thinking of the numbers to be added, arranging them into a rectangle, then finding the area of the rectangle.
For the first powers, he uses two copies of each.
So the final sum is half the area of the rectangle.
Visit Mathematical Intentions at http://www.quadrivium.info to learn about how calculus developed from this technique.