0 _1 11 4114-1 n+1 In this problem, we investigate the power series 2 wal)' n20 1)n4n+1$ n+1 ( (a) Show that Z \" 110 3 +1(n + 1) centred on a: = 0. 4 is the Taylor series for the function f (1:) = ln (3; + 1) 4 (b) For which values of a: is the series equal to In ( Z: + 1)? 1)n4n+1$ n+1 1Mn4n+1 n+5 (c) If we multiply the series by 3:4 we get 3134:0(3+1(+1)= g(3 +1( + 1), ,a re \" n n (n 43: lated power series, which is equal to a: 41n \"(3 + 1) on the same interval you identied in part b. 4 Express [41: 1n ( 5+1) d1: as a power series in .13. (d) Let g(:1c) :1: 4111 (ll5+ Consider, but do not give a response to the question: should you nd the Maclaurin series for g'(a:) directly, or by starting from the series in (c)? 1) . Find g'(a:), and the Maclaurin series for g'(1:)