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 s_k as k→∞? Does your CAS find a closed form answer for this limit?

b. Plot the first 100 points (k, s_k) 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, s_k). Discuss the behavior in your own words.

d. Plot the first 400 points (k, s_k). What happens when k = 355? Calculate the number 355/113. Explain from you calculation what happened at k = 355. For what values of k would you guess this behavior might occur again?

Transcribed Image Text:

∞ Σ n=1 1 n³ sin² n