Please need an answer with steps asap

The function f(x) = 4x In(1 + 2x) is represented as a power series f (z) = > cnach n=0 Find the FOLLOWING coefficients in the power series. Co = C1 C3 = C4 = Find the radius of convergence R of the series. R =\\ Match each of the Maclaurin series with right function. (1. (-1) 2 2 2n+1 no (2n + 1)! 2. 7 0 3.(-1) "2x 2+1 7 0 2n + 1 (-1)"22 2n 4. (2n) ! A. e2x B. cos(2x) C. 2 arctan(2) D. 2 sin(x) 27 Use the ratio test to determine whether converges or diverges. n-19 (572)2 (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n > 19, lim an+1 lim an (b) Evaluate the limit in the previous part. Enter oo as infinity and -co as -infinity. If the limit does not exist, enter DNE. lim an+ 1 100 + 21 an (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose - 2 correct answers