Write the First Five Terms of the Power Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x - 8 ) ^ { n } } { 4 ^ { n } }$

question 88

Multiple Choice

Write the first five terms of the power series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x - 8 ) ^ { n } } { 4 ^ { n } }$ .

• A) \(\frac { ( x - 8 ) } { 4 } - \frac { ( x - 8 ) ^ { 2 } } { 4 ^ { 2 } } + \frac { ( x - 8 ) ^ { 3 } } { 4 ^ { 3 } } - \frac { ( x - 8 ) ^ { 4 } } { 4 ^ { 4 } } + \frac { ( x - 8 ) ^ { 5 } } { 4 ^ { 5 } }\)
• B) \(- \frac { ( x - 8 ) } { 4 } - \frac { ( x - 8 ) ^ { 2 } } { 4 ^ { 2 } } - \frac { ( x - 8 ) ^ { 3 } } { 4 ^ { 3 } } - \frac { ( x - 8 ) ^ { 4 } } { 4 ^ { 4 } } - \frac { ( x - 8 ) ^ { 5 } } { 4 ^ { 5 } }\)
• C) \(- \frac { ( x - 8 ) } { 4 } + \frac { ( x - 8 ) ^ { 2 } } { 4 ^ { 2 } } - \frac { ( x - 8 ) ^ { 3 } } { 4 ^ { 3 } } + \frac { ( x - 8 ) ^ { 4 } } { 4 ^ { 4 } } - \frac { ( x - 8 ) ^ { 5 } } { 4 ^ { 5 } }\)
• D) \(\frac { ( x - 8 ) } { 4 } + \frac { ( x - 8 ) ^ { 2 } } { 4 ^ { 2 } } + \frac { ( x - 8 ) ^ { 3 } } { 4 ^ { 3 } } + \frac { ( x - 8 ) ^ { 4 } } { 4 ^ { 4 } } + \frac { ( x - 8 ) ^ { 5 } } { 4 ^ { 5 } }\)
• E) \(- \frac { ( x - 8 ) } { 4 } - \frac { ( x - 8 ) ^ { 2 } } { 4 ^ { 2 } } + \frac { ( x - 8 ) ^ { 3 } } { 4 ^ { 3 } } + \frac { ( x - 8 ) ^ { 4 } } { 4 ^ { 4 } } - \frac { ( x - 8 ) ^ { 5 } } { 4 ^ { 5 } }\)

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Definitions:

Stages of Development

The concept of progressive phases individuals go through during their psychological, physical, or social maturation process.

Interpersonal Attraction

The force that draws individuals together, leading to friendships, romantic relationships, or other forms of social connections.

Cohesion

The degree to which members of a group are connected to each other, fostering unity and a sense of belonging.

Punctuated Equilibrium Model

A theory in evolutionary biology and political science suggesting that changes occur in rapid, significant bursts followed by periods of stability.