The University of Western Ontario (Western University) Calculus 1501B, Winter 2014 Homework assignment 3 (22 marks total). Due on Tuesday March 11, in class. [Note: this assignment will not be marked before March 14th but the solutions will be posted on Wed. March 12.] Problem 1. (4 marks) Use the Integral Test to determine whether each of the following series is convergent or divergent: (a) n2 n=1 1 + 4n + 9 1 2 n1 (b) n=1 Problem 2. (4 marks) Use the Comparison Test to determine whether the series is convergent or divergent arctan n (a) n3 n=1 1 n 0.3 (b) n=1 Problem 3. (4 marks) Use the Limit Comparison Test to determine whether each of the following series is convergent or divergent (a) n=1 (b) n=1 en + n 5n + 3 n n + cos n n2 n + n + 1 1 Problem 4. (4 marks) Use the Alternating Series Test to test the series for convergence (1)n1 e2n n=1 Is it absolutely convergent ? If so, what is n=1 e2n ? Problem 5. (2 marks) Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 1 (1)n 0.2 n n=1 Problem 6. (4 marks) (a) Use the Ratio Test to determine whether the series is absolutely convergent or divergent: n3 n n=1 (2) (b) Use the Root Test to determine whether the series is absolutely convergent or divergent: 2 ln n + en en n n=5 ln n + | sin( 3 )| 2