Purdue MA166 Spring 2022 Exam 3 Question 6

Why is II conditionally convergent? In other words, could you explain why sin(pi/(k^(1/3))) diverges?

Purdue MA 16600 c X P Purdue University: [ X serve_file.php X serve_file.php X Sy sum from n=1 to in X P Purdue University: [ X + X @ https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.php?file= 16600E3-$2... Yo G G . . . 9 of 15 Q T A v MA 16600 Exam 3 , Page 7 of 13 Spring 2022 6. Determine whether the following series are absolutely convergent, conditionally conver- gent, or divergent: I. [(-1)k+1 cos (" II. (-1)*+1 sin (1/3, III. COS (KT) k3 + 1 A. I is divergent; II and III are absolutely convergent B. I and II are divergent; II is absolutely convergent C. I is divergent; II is conditionally convergent; III is absolutely convergent D. I is divergent; II and III are conditionally convergent E. I and III are absolutely convergent; II is divergent ENG 7:20 PM US 7/5/2022 2