MATH 262 Midterm: MATH 262 Midterm 3 Fall 2018 Solutions

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 262
• Professor: All

Document Summary

3x 1 (x + 3)(x 2) in partial fractions. (ii) (5 points) determine explicitly the coef cient of xn in the power series expansion of. 3x 1 (x + 3)(x 2) about x = 0. (iii) (3 points) find the radius of convergence of the expansion. Either use the ratio test or explain your reasoning. B x 2 which leads to 3x 1 = a(x 2) + b(x + 3). Equating coef cients gives 1 = 2a + 3b and 3 = a + b. Solving gives a = 2 and b = 1. Alternatively the method of residues can be used (i. e. one substitutes rst x = 3 and then x = 2 into 3x 1 = a(x 2) + b(x + 3)). (ii) at this point, we have. 3(cid:19)n (iii) from the known fact that the maclaurin series for (1 u) 1 has radius 1, we can deduce that the.