MARKED PROBLEM (-1 )24ntlyn+1 In this problem, we investigate the power series n=0 3n+1(n + 1) 18 (a) Show that E 3n+1(n + 1) -is the Taylor series for the function f(x) = In +1 n=0 centred on r = 0. (b) For which values of a is the series equal to In 3 + 1 ) (c) If we multiply the series by ' we get a*) (-1 )nantlan+1 (-1 )nan+lyn+5 3n+1(n + 1) -, a re- n=0 n=0 3n+1(n + 1) lated power series, which is equal to x In 4.x 3 + 1 on the same interval you identified in part b. Express x In (2 + 1 ) dx as a power series in T. (d) Let g(x) = x4 In + 1. Find o'(x), and the Maclaurin series for g'(z). Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)