## Infinite Series in Fractals

The square has side length 1. The triangles inside the square are isosceles right triangles.
is the first partial sum:
- It is the sum of the areas of the blue and red triangles when n = 1
- Compute
2. is the second partial sum:
- move the slider to n = 2
- find the areas of the new triangles
- add them to to find
3. Compute three more partial sums
4. What is the series that corresponds to the area of the red and blue shaded region as n goes to infinity?
5. What is the area of the red and blue shaded region as n goes to infinity?

**Hint:***If you draw the diagonals of the middle square, you should notice that 8 congruent right isosceles triangles make up the whole square. This should help you find the area of the shaded triangles.*1.