Question

Suppose a bouncy ball is shot into the air and bounces in such a way that the height of the nth bounce is given by Sn = 1/ (n^2+4) meters. Suppose the ball bounces indefinitely. Find an approximation to the total distance traveled by the ball so that the error less than .0001.
This problem has several stages

1) First you need to find a series which represents the total distance traveled by the ball. (Remember the ball goes up and down. . .) Explain where the series comes from as part of the write-up.

Answer 1

2) Next, you need to use the integral test to show that the series converges. Why is this step necessary?

3) Choose a reasonably large N and approximate the series using a partial sum. You can use a calculator or Wolfram Alpha for this part.

4) Compute an estimation of your error. If it’s more than .0001 you need to redo the previous part.

Answer 2

Above, you have a representation of the given series \(\displaystyle\sum_{n=1}^\infty \frac{1}{n^2+4}\). The sketch only gives you the upward distance traveled. How can you account for the downward distance, provided that it's the same as the upward distance?

Answer 3

could you explain more plz with details how is it work