Write the Statements S₁, S₂, and S₃ and Determine If $$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

question 152

Essay

Write the statements S₁, S₂, and S₃ and determine if each statement is true.
- $$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

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Definitions:

Observational Learning

The process of acquiring new behaviors or information through watching and imitating the actions of others, also known as social learning.

Classical Conditioning

An educational method where two stimuli are consistently linked together, leading to a response initially triggered by the second stimulus but later induced by the first stimulus alone.

Operant Conditioning

A learning process in which the consequences of an action determine the likelihood of that action being repeated in the future.

Observational Learning

Acquiring knowledge by watching the actions of other people.