Find the Fifth Partial Sum S₅ of the Given Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 3 ^ { n } }$

question 6

Multiple Choice

Find the fifth partial sum S₅ of the given series. $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 3 ^ { n } }$

• A) \(- \frac { 121 } { 243 }\)
• B) \(- \frac { 40 } { 81 }\)
• C) \(- \frac { 61 } { 243 }\)
• D) \(- \frac { 20 } { 81 }\)

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Definitions:

Interchangeable

Capable of being substituted or replaced by another similar item, implying a degree of similarity and mutual substitutibility.

Idiosyncratic Deals

Customized work arrangements negotiated between an employee and employer to cater to specific individual needs or skills.

Disrupting

The act of causing a disturbance or interruption in a process, event, or situation.

Sense of Fairness

An individual's perception of the equity or justice of a situation, affecting their satisfaction with outcomes.