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) \(\frac { 1 } { 6 } \sum _ { n = 0 } ^ { \infty } \left( \frac { - 1 } { 6 } \right) ^ { n } \frac { ( x ) ^ { n + 1 } } { n + 1 }\)

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Halo Effect

A cognitive bias where an observer's overall impression of a person, brand, or product positively influences their feelings and thoughts about that entity's specific traits.

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The systematic assessment of an individual's job performance and productivity, typically based on criteria such as quality of work, efficiency, and goal achievement.

Fundamental Attribution Error

The tendency to over-emphasize personality-based explanations for behaviors observed in others while under-emphasizing the role of external situations.

Internal Explanations

The justifications or reasons for phenomena, actions, or decisions that originate from within an individual or organization.