Use Mathematical Induction to Prove That the Statement Is True $$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

question 55

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

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Definitions:

Market Share Theory

A principle that assigns liability to manufacturers based on their market share of a harmful product when the specific source of harm cannot be identified.

Tortfeasors

Individuals or entities that have committed a tort, which is a civil wrong or injury that can be redressed by awarding damages.

Allegedly Harmful Products

Allegedly harmful products are goods reported or claimed to cause damage or injury, often subject to investigation or legal action to ascertain liability.

Assumption Of Risk

A defense in tort law that a person may not recover for damages suffered from risks they understood and voluntarily chose to accept.