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:

Intermittent Reinforcement

A conditioning schedule in which a behavior is rewarded at random intervals, which can lead to a high level of response persistence.

Desired Behaviour

The specific actions or reactions that an organization or individual aims to elicit from others, typically to achieve a certain goal or outcome.

Reinforcement Schedule

A pattern that determines how often a desired behavior is reinforced in operant conditioning, influencing how quickly and robustly that behavior is learned.

Negative Reinforcement

A behavioral principle where the removal of an unfavorable outcome or stimulus strengthens a desired behavior.