Problem 1. Consider the geometric series where the real number 1' gives the ratio between successive terms. Note that the series starts with k=0ratherthank= 1 (a) Let r = g and use Sage to investigate the partial sums of the series As you evaluate partial sums with more and more terms, what appears to be the limiting value? Conrm that this value for the sum of the innite series agrees with the well-known formula for the sum of a geometric series whose ratio r has absolute value less than 1. (Found in Section 10.3 of your text) owl-l:- (b) Let r = 1.01 and use Sage to study the partial sums. What do you conclude about the convergence or divergence of the geometric series in this case? Explain. (c) Now let 1- = 1 and r = 1. Discuss the convergence or divergence of the series in these cases. Do you really need to use a computer in part c or even in part b? Explain. (d) When r is negative in a geometric series we get an example of an alternating series. Explain why this is an aptly chosen description. Give examples of two alternating geometric series, one convergent and one divergent. (e) Investigate the behavior of the geometric series for various values of the ratio 1'. Write a clear and complete statement summarizing your results