Use Mathematical Induction to Prove That the Statement Is True $$4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$$

question 340

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$$

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Definitions:

Visceral Responses

Automatic, instinctive bodily responses to stimuli, typically related to emotions and survival such as fear or hunger, mediated by the autonomic nervous system.

Skeletal Responses

Skeletal responses refer to reactions or movements of the skeletal muscles, which can be voluntary or involuntary, often as a response to various stimuli.

Reflexive Responses

Involuntary, automatic actions or processes in response to a stimulus.

Puzzle Boxes

Mechanical boxes that are designed to be opened through a series of manipulations as part of a problem-solving task, often used in animal behavior studies.