MATH 181 Study Guide - Final Guide: Partial Fraction Decomposition, Horse Length, Eaves
Document Summary
Problem 1 solution: find the sums of the following series. (a) (b) We begin by decomposing the summand using partial frac- tions. The nth partial sum of the series is: n (cid:18) 1 k + 2. 5(cid:19) + +(cid:18) 1 n + 2. 1 n + 3(cid:21) (b) this is a sum of two geometric series. We begin by rewriting the series as follows: In the rst series on the right hand side, we have r = 2 starts at k = 2, the sum is e and a = 1. In the second series on the right hand side, we have r = 1 starts at k = 2, the sum is e and a = 4. Problem 2 solution: evaluate each integral or show that it diverges. Solution: (a) the rst step we take is to convert the integral into a limit calculation: 1 x x4 + 1 dx = lim b z b.
