Question 384386
I think I have solved this exact same question previously on this website. Here is my solution:

This is equivalent to finding the power series of ln x centered around x = 1. Note that all derivatives of ln x at x = 1 are equal to 1 or -1. Since we have the power series

{{{ln (x) = (x-1) - ((x-1)^2)/2! + ((x-1)^3)/3! - ...}}}

Adding one to all the x terms produces the given result.