Convergent Geometric Series Pile Driver Problem: A pile driver pounds a piling (a

Chapter 14, Problem 3

(choose chapter or problem)

Convergent Geometric Series Pile Driver Problem: A pile driver pounds a piling (a column) into the ground for a new building that is being constructed (Figure 14-3a). Suppose that on the first impact the piling moves 100 cm into the ground. On the second impact the piling moves another 80 cm into the ground. Assume that the distances the piling moves with each impact form a geometric sequence. Figure 14-3a a. How far will the piling move on the tenth impact? How far into the ground will it be after ten impacts? b. Run the partial sums program using n = 100. What do you notice about the partial sums as the grapher displays each one? What does it mean to say that the partial sums are converging to 500? What is the real-world meaning of this limit to which the series converges? c. Show how to calculate algebraically that the limit to which the partial sums converge is 500.