The Series Can Be Used to Estimate the Value of Ln(a) for 1

Multiple Choice

The series $\ln ( x ) = ( x - 1 ) - \frac { ( x - 1 ) ^ { 2 } } { 2 } + \frac { ( x - 1 ) ^ { 3 } } { 3 } - \ldots + ( - 1 ) ^ { n - 1 } \frac { ( x - 1 ) ^ { n } } { n }$ can be used to estimate the value of ln(a) for any positive real number a such that $0 < \mathrm { a } \leq 2$ . Use the first five terms of this series to estimate $\ln ( 1.17 )$ . Round to the nearest thousandth.

A) $1.047$
B) $1.717$
C) $0.157$
D) $- 0.773$