Assignment:
Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8, ......to find the following:
a. What is r, the ratio between 2 consecutive terms?
b. Using the formula for the sum of the first n terms of a geometric series. What is the sum of the first 10 terms? Please round your answer to 4 decimals.
c. Using the formula for the sum of the first n terms of a geometric series. What is the sum of the first 12 terms? Please round your answer to 4 decimals.
d. What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Provide complete and step by step solution for the question and show calculations and use formulas.