Use the Principle of Mathematical Induction to Show That the Statement

question 74

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- $$1 + 3 + 3 ^ { 2 } + \ldots + 3 ^ { n - 1 } = \frac { 3 ^ { n } - 1 } { 2 }$$

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Definitions:

Respondeat Superior

A legal doctrine that holds employers or principals liable for the actions of their employees or agents conducted within the scope of their employment or agency.

Indemnification

A provision where one party agrees to compensate another for any loss or damage incurred, often seen in contracts.

Substantial Departure

A significant deviation or movement away from a previously set course or standard, often used in legal or regulatory contexts.

Extremely Hazardous Activities

Activities that pose significant risk of causing substantial harm, often requiring stricter liability standards in tort law.