MAC 2312 Midterm: MAC2312 C08 Test 4
Document Summary
Instructions: write your complete solutions on your answer paper. No graphing calculators are allowed to be used. You are not required to simplify your answers. (1) (10 pts. ) Find a formula for the nth partial sum of the series. If it converges, nd the sum. (2) (20 pts. ) For the following, determine whether the series converges or di- verges. For each convergent series, nd the sum. (a) Use your answer to determine whether the series. 1 n(ln n)2 converges or diverges. (4) (20 pts. ) For the following, determine whether the series converges abso- lutely, converges conditionally, or diverges. (a) For each power series, nd the interval of convergence. (a) Xn=0 (n + 1)(x 1)n n + 2 (b) For f (x) = x + 1, nd the rst four derivatives f (x), f (x), f (x), f (4)(x). Use these to nd the taylor polynomial of order four for f (x) centered at a = 0.
