Express the Sum Using Summation Notation $$\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$$

question 56

Multiple Choice

Express the sum using summation notation.
- $$\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$$

• A)
• \[\sum _ { k = 1 } ^ { n } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\]
• B)
• \[\sum _ { k = 1 } ^ { 14 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\]
• C)
• \[\sum _ { k = 1 } ^ { 13 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\]
• D)
• \(\sum _ { k = 1 } ^ { 13 } \left( \frac { 4 } { 5 } \right) ^ { k }\)

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Definitions:

Reciprocation

Reciprocation involves the mutual exchange of actions, goods, services, or feelings, often as part of social or relationship norms.

Disrupt-then-reframe Technique

A persuasive strategy involving the initial disruption of normal thought processes followed by offering a new frame or perspective that makes the initial proposition more acceptable.

Pique Technique

Influence technique in which one captures people’s attention, as by making a novel request.

Foot-in-the-door Technique

A persuasion strategy where one starts with a small request to increase the likelihood of agreement to a larger request later.