Write the Word or Phrase That Best Completes Each Statement $1 + 6 + 6 ^ { 2 } + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$

question 6

Essay

Write the word or phrase that best completes each statement or answers the question.
Use mathematical induction to prove the following statement for all positive integers n.
- $1 + 6 + 6 ^ { 2 } + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$

Analyze the role of social support and resources in mitigating the effects of stress on relationships.

Examine the influence of external stress on communication and perception within relationships.

Describe the impact of socio-economic factors on relationship stability and quality.

Explore the role of social networks in supporting or challenging intimate relationships.

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Definitions:

Diseconomies of Scale

The situation in which a business grows to a point where the costs per unit increase, opposed to saving costs, often due to managerial inefficiencies or complexity.

Constant Returns to Scale

A situation in which increasing the amount of all inputs used in production by a certain factor results in output increasing by the same factor.

Economies of Scale

Cost advantages that enterprises obtain due to their size, output, or scale of operation, with cost per unit of output generally decreasing with increasing scale.

Diseconomies of Scale

A condition when a company or business grows so large that the costs per unit increase, leading to reduced efficiency.