Can you solve this step by step? I would like to verify my answers and have a more in-depth work if I didn't get the right solution.

Math 143 Midterm 1 Sample Questions 1. Do these series converge? If so, why? And - 2 a. 1 2 304 + 2 b. 712 + 1 (Inn)" d. (1+n)3 e. (1+ vn)* Inn 2. Find the interval and radius of convergence for these series a. In/2x b. [ ( x + 4 ) " / n" 3. Let /(x) = \\5 + 2x. a. Find the degree 2 Taylor polynomial for A(x). b. Find a bound on the error when approximationg f(1) by taking x = 1 in part a. 4. Approximate the value of (-1)" Inn - to within 1/1000 of the true value. (The answer may be left as 1-1 a finite sum of fractions with . .. in the middle). 5. Using the well known series for e", sin x, and 1/ (1 - x), find the power series for these functions: Sinx - x a. 4x2 6. Find the exact values of _ (-1)" 3 7