Integrate the Series For $\frac { 1 } { x + 6 }$

question 118

Multiple Choice

Integrate the series for $\frac { 1 } { x + 6 }$ to find the power series for the function $f ( x ) = \ln ( x + 6 )$ .

• A) \(\frac { 1 } { 7 } \sum _ { n = 0 } ^ { \infty } \left( \frac { - 1 } { 7 } \right) ^ { n } \frac { ( x ) ^ { n } } { n + 1 }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( 6 x - 1 ) ^ { n - 1 } } { n - 1 }\)
• C) \(\frac { 1 } { 6 } \sum _ { n = 0 } ^ { \infty } \frac { ( x ) ^ { n + 1 } } { n + 1 }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( 6 x - 1 ) ^ { n } } { n - 1 }\)
• E) \(\frac { 1 } { 6 } \sum _ { n = 0 } ^ { \infty } \left( \frac { - 1 } { 6 } \right) ^ { n } \frac { ( x ) ^ { n + 1 } } { n + 1 }\)

---

Definitions:

Widgets

A generic term often used to refer to any product, especially a hypothetical one used for economic or teaching purposes.

Tax

A mandatory monetary fee or another form of charge levied on a taxpayer by a government body to finance government operations and various public expenses.

Elastic

Describes a situation in which the demand or supply of a good or service is highly sensitive to changes in price.

Radish Farmers

Individuals or businesses involved in the cultivation and sale of radishes, typically as part of the agricultural sector.