Consider the sequence where each successive term is determined by adding 1 to each of the numerator and denominator.

1. What are the fourth and fifth terms of this sequence?

2. Compute the ratio of the second term to the first, the ratio of the third term to the second, the ratio of the fourth term to the third, and the ratio of the fifth term to the fourth.

3. Evaluate each of the ratios you computed in Exercise 2 for x = 0, 10, and 100.

4. What seems to be happening to the ratios as the value of x increases? Explain.

5. Form a new sequence with the first term , but for which the successive terms are determined by subtracting 1 from each of the numerator and denominator.

6. Compute the ratios of successive terms of the new sequence.

7. Evaluate each of the ratios you computed in Exercise 6 for x = 0, 10, and 100.

8. What seems to be happening to the ratios as the value of x increases? Explain.