Use the Binomial Series to Find the Maclaurin Series for the Function

question 58

Multiple Choice

Use the binomial series to find the Maclaurin series for the function
$f ( x ) = \frac { 8 } { ( 1 + x ) ^ { 2 } }$

• A)\(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 + 8 \sum _ { n = 0 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } n ! }\)
• B)\(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 + 8 \sum _ { n = 1 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } n ! }\)
• C) \(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 + 8 \sum _ { n = 0 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { n ! }\)
• D) \(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 \sum _ { n = 0 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } n ! }\)
• E)\(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 \sum _ { n = 1 } ^ { \infty } \frac { ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } }\)

Recognize the role of self-awareness and self-regulation in listening.

Understand and apply analytical and critical listening in varying situations for effective communication.

Understand the concept of environmental cues in association with rewards.

Comprehend the factors motivating escape behavior and the approach towards reward.

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Definitions:

Psychological Environment

The perceived or experienced surroundings that influence an individual's mental and emotional state.

Force

The influence or energy exerted on or against an object in order to cause it to change its motion or state.

Learning

The process of acquiring new understanding, knowledge, behaviors, skills, values, or preferences through study, experience, or teaching.

Probability

A measure or estimation of how likely it is that an event will occur, expressed as a value between 0 and 1.