imo, "can visualize". In my experience, those strong in math easily visualize math problems geometrically. This is opposed to, for example, having to grind thro

imo, "can visualize". In my experience, those strong in math easily visualize math problems geometrically. This is opposed to, for example, having to grind through the quadratic formula. Try to mentally (or on paper) graph the freelancer's pay. The x-axis represents "hours" and the y-axis represents "pay per hour". The function we get is the linear function "f(x) = x". I.e. for the first hour, he's paid $1; for the 300th hour, he's paid $300. A very straightforward graph. If we cut off our x-axis at $300, the graph looks like a right triangle. If you want to find the total amount of money he's accumulated, all you have to do is find the area under the triangle (which is a special case of integration). For a triangle, geometry class taught us "Area = (1/2)(base)(height)". Calculus courses prefer that we integrate, which has broader application. Integration of "f(x) = x" gives us "f'(x) = (1/2)(x^2)". Our "integral" is equivalent to the "geometry-class equation" because for our particular triangle, the base is the same as the height. For comparison: Area = (1/2)(base)(height) f'(x) = (1/2)(x^2) DoubleMalt is saying kjay's visualized "shortcut" (intuitively faster approximation) is slightly off. This is because the triangle in our actual problem looks like a staircase, and not a smooth slope. But kjay's shortcut has a margin of error of only about "-0.033%" which is a good enough approximation by most people's standards. Also, DoubleMalt's equation should look like x * (x + 1) / 2 instead of x * (x - 1) / 2