A Statement Sn About the Positive Integers Is Given $$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

question 38

Essay

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements 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:

Confirmation Bias

A cognitive bias that causes people to search for, interpret, favor, and recall information in a way that affirms their preexisting beliefs or hypotheses.

Development

Refers to the process of growth, progress, or evolution in any aspect, including physical, psychological, or social phenomena.

Daycare

A service that provides care and supervision for children during the daytime, often allowing parents to work or engage in other activities.

Negative Correlation

A relationship between two variables in which one variable increases as the other decreases, indicating an inverse association.