Find a Formula for the Nth Partial Sum of the Series

question 104

Multiple Choice

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
- $$2 + \frac { 2 } { 7 } + \frac { 2 } { 49 } + \ldots + \frac { 2 } { 7 ^ { n - 1 } } + \ldots$$

• A) \(\frac { 2 \left( 1 - \frac { 1 } { 7 ^ { n - 1 } } \right) } { 1 - \frac { 1 } { 7 } } ; \frac { 7 } { 4 }\)
• B) \(\frac { 2 \left( 1 - \frac { 1 } { 7 ^ { n } } \right) } { 1 - \frac { 1 } { 7 } } ; \frac { 7 } { 3 }\)
• C) \(\frac { 2 \left( 1 - \frac { 1 } { 7 ^ { n } } \right) } { 1 - \frac { 1 } { 7 } } ; \frac { 7 } { 4 }\)
• D) \(\frac { 2 \left( 1 - \frac { 1 } { 7 ^ { n - 1 } } \right) } { 1 - \frac { 1 } { 7 } } ; \frac { 7 } { 3 }\)

Acknowledge the role of portfolio planning in strategic management and its goal in resource allocation.

Grasp the dynamic nature of product life cycles and the need for strategic adjustment.

Comprehend the importance of competitive advantage and the conditions for its development.

Understand the principles of corporate governance and its impact on strategic planning and implementation.

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Definitions:

Trap Game

A situation in sports where a stronger team underestimates a seemingly weaker opponent, often leading to an unexpected loss.

Negative Situation

Describes an event, circumstance, or condition perceived as unfavorable, harmful, or detrimental.

Victim

Someone who has been harmed, injured, or negatively affected by another person or situation, often resulting in suffering or disadvantage.

Harm

Physical injury, damage to health, or emotional distress caused by actions or events that negatively affect well-being.