1. Use any method to determine whether the following series converges or diverges. (4 points each) (a) (-1)" n=1 ( b ) (-1)n+1 (n + 1) In(n + 1) sin 2. Determine if the series 2 iM 8 is absolutely or conditionally convergent. (5 points) Vn 2 3. Determine the interval of convergence of (x - 3)n 2n + 1 . -. (5 points) n=1 4. Does the Taylor series expansion of f(x) = (1 + 3x)24 about a = 1 have only a finite number of terms? Briefly explain/justify your answer. (3 points) 5. Consider the function defined by f(x) = 10g3(2x - 1). a. Determine the Taylor series expansion about a = 1. (5 points) b. Find all possible values of a so that the Taylor series expansion of a is well-defined. (2 points) c. Using the first five terms of the Taylor series, approximate the value of f(2). Compare it with the actual value of f(2). (2 points)