Use the Principle of Mathematical Induction to Show That the Statement

question 88

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers 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:

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A developmental phase following adolescence, typically marked by increased independence and responsibilities in early adulthood.

Late Adolescence

The final stage of adolescence, typically ages 18-21, characterized by increased independence, identity exploration, and the transition into adulthood.

Adult Status

The phase of life characterized by having obtained the social, legal, and developmental traits typically associated with adulthood, such as independence and responsibility.