a) Write the taylor series expansion about x = 0 for f(x) = ln(1+x). Include an expression for the general term.

b) Find the radius of convergence for the series in part a). Justify your answer.

c) Estimate the error in evaluating ln(3/2) by using only the first five nonzero terms of the series in part a). Justify your answer.

d) Use the result found in part a) to determine the logarithmic function whose Taylor series is the sum from n=1 to infinity of ((-1)^(n+1)x^2n)/(2n)