Infinite geometric series

1. a) Write the repeating decimal, 0.0808… as a geometric series .

b) Write its sum as the ratio of two integers.

2. A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance traveled by the ball.

3. The sides of a square are 16 inches in length. A new square is formed by connecting the midpoints of the sides of the original square, and two of the triangles outside the second square are shaded. Sketch a model of the square and determine the area of the shaded regions

(a) if this process is continued five more times and (b) if this pattern of shading is continued indefinitely.