Use Mathematical Induction to Prove That $2 \mid \left( n ^ { 2 } + n \right) \text { for all } n \geq 0 \text {. }$

question 51

Essay

Use mathematical induction to prove that $2 \mid \left( n ^ { 2 } + n \right) \text { for all } n \geq 0 \text {. }$

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Definitions:

Perfectly Price Discriminate

A theoretical market condition where a seller charges each buyer their maximum willingness to pay, capturing all potential consumer surplus.

Perfectly Price Discriminates

A pricing strategy where a seller charges the maximum possible price for each unit consumed that the buyer is willing to pay, capturing the entire surplus.

Consumer Surplus

The variance between the aggregate amount consumers intend and have the means to pay for a good or service and the sum they actually pay.

Consumer Surplus

The gap between what consumers are prepared and able to spend on a product or service and the actual amount they end up paying.