1. (8 points) Sections 5.1-5.2 a. Show that the sequence 97 n! converges. b. Show that the series (-1)" converges. n 2. (16 points) Sections 5.4 5.5 Determine the appropriate Taylor series expansion for the following functions. a. log(z + 21), zo = 0 b. z2ez - 2zet + ez, zo = 1 c. z sin z2, zo = 0 d. cosh z, zo = 0 3. (16 points) Sections 5.4-5.5 Use the ratio test to determine the radius of convergence (denote by R) in each of the cases in the previous question. 4. (5 points) Section 5.4 5.5 Determine the first three terms in the Taylor series expansion of v z2 - 1 about zo = 0 by using Newton's binomial formula (Newton's generalized binomial theorem). Choose the branch of square root so that v-1 = 2. What is the radius of convergence