How many terms of the Taylor series for ln (1 + x) should you add to be sure of calculating ln (1.1) with an error of magnitude less than 10^-8? Give reasons for your answer.

Question

How many terms of the Taylor series for ln (1 + x) should you add to be sure of calculating ln (1.1) with an error of magnitude less than 10^-8? Give reasons for your answer.