midterm - Math 21C Sec 002 Midterm Exam Name Student ID...

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Math 21C - Sec 002 Midterm Exam July 12, 2007 Name .......................................... Student ID Number ............................ Math 21C Midterm - Summer Session 1 Instructor: Stephen Ng Instructions: 1. You have 1 hour to complete this exam. Budget your time wisely. 2. The exam is to be closed book and closed notes, except for an approved 8.5 × 11 handwritten sheet. 3. No calculators are allowed. 4. Show all work. Answers without proper justification will receive no credit. 5. Do not write things that you know to be false. Partial credit will be given for proper application of inconclusive tests. 6. Negative points will be rewarded for committing the ultimate sin! Remember that the n th term test can only be used for divergence. Question Points Score 1 20 2 20 3 20 4 20 5 20 6 20 Total: 120
Math 21C - Sec 002 Midterm Exam July 12, 2007 1. (20 points) The Taylor series for ln(1 + x ) is n =1 ( - 1) n - 1 x n n = x - x 2 2 + x 3 3 - · · · + ( - 1) n - 1 x n n + · · · (a) Find the radius of convergence and the interval of convergence. For which points is the convergence absolute? For which points is the convergence conditional?