Find the nth degree taylor polynomial for f x centered a 0

Question

This problem asks for Taylor polynomials for f(x) = In(1+ x) centered at a = 0. Show your work in an organized way.

(a) Find the 4^th, 5^th and 6^th degree Taylor polynomials for f(x) centered a = 0.

(b) Find the n^th degree Taylor polynomial for f (x) centered a = 0, written in expanded form.

(c) Find the n^th degree Taylor polynomial for f (x) centered a = 0, written in summation notation.

(d) Use the 7^th degree Taylor polynomial to estimate ln (2).

(e) Compare your answer to the estimate for ln (2) given by your calculator. How accurate were you?