- L. Marizza A. Bailey
- Geometry, Mathematics, Sequences and Series
Infinite Series in Fractals
The square has side length 1. The triangles inside the square are isosceles right triangles. 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. 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?