Please answer all questions and show work:

1) Evaluate the following as true or false. O true 1 O false The series converges. K 2 (In k) 2) For the ratio test to indicate absolute convergence, which of O p =0 the following must be true? Op 1 3) The degree of a Taylor polynomial is f" (c) equal to the value of k in Of (c) + f' (c)(x- c) +- 2 (I- C)2 f(") ( c) Of' (c) (x - c) + f" (c) f ( x) = E 2 (I - C)2 n! (I - c)" O f(c) + f' (c) (1- Which of the following expressions O f" (c) 2 (2- c)2 correctly states the second-degree Taylor polynomial in expanded notation? 4) Find the radius and interval of O Radius = 1, Interval = (0, 2] convergence of M8 (-1)" (x - 1)" Radius = 1, Interval = [0, 2] (n + 1) In(n + 1) O Radius = 1, Interval = [0, 2) O Radius = 1, Interval = (0. 2)