Let's put a little geometry into geometric series! The spiral in the picture is
made from 45° right triangles. The smallest triangle (red) has a side length of
1. You can use the Pythagorean theorem to find that the length of its
hypotenuse is 2. The next (orange) triangle has a side length exactly
matching the hypotenuse of the smallest triangle (which was just mentioned
as being 3). The next (yellow) triangle has a side length of 2; the next
triangle has a side length of 22, and so on.
The areas of the colored triangles, calculated with the formula
1. base height, are 1, 1, 2, 4, and so on. What is the area of this entire
colorful figure?
If necessary, use the slash bar to enter fractions. Reduce fractions to their
lowest terms.