COMPUTER EXPLORATIONSIt is not yet known whether the
Chapter 10, Problem 71E(choose chapter or problem)
Problem 71E
COMPUTER EXPLORATIONS
It is not yet known whether the series
converges or diverges. Use a CAS to explore the behavior of the series by performing the following steps.
a. Define the sequence of partial sums
What happens when you try to find the limit of sk as k →∞? Does your CAS find a closed form answer for this limit?
b. Plot the first 100 points (k, sk) for the sequence of partial sums. Do they appear to converge? What would you estimate the limit to be?
c. Next plot the first 200 points (k, sk) Discuss the behavior in your own words.
d. Plot the first 400 points (k, sk) What k = 355? happens when Calculate the number 355/ 113. Explain from your calculation what happened at k = 355.For what values of k would you guess this behavior might occur again?
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