Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-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 $\ln ( \mathrm { a } )$ for any positive real number a such that $0

Question

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-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 $\ln ( \mathrm { a } )$ for any positive real number a such that $0 < \mathrm { a } \leq 2$. Use the first five terms of this series to estimate $\ln ( 0.86 )$. Round to the nearest thousandth.
A) $- 1.081$
B) $0.739$
C) $- 0.151$
D) $1.409$

Quizplus · Accepted Answer

The first five terms of the series for $\ln(0.86)$ are calculated as follows: $(0.86 - 1) - \frac{(0.86 - 1)^2}{2} + \frac{(0.86 - 1)^3}{3} - \frac{(0.86 - 1)^4}{4} + \frac{(0.86 - 1)^5}{5}$. Evaluating these terms and summing them gives approximately $-0.151$.

Graph the Function Corresponding to the Sequence Defined Can Be Used to Estimate the Value Of