Use Mathematical Induction to Prove That the Statement Is True $$1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

question 532

Essay

Use mathematical induction to prove that the statement is true for every positive integer 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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North American Colonies

The North American Colonies refer to the territories in North America that were colonized by European powers from the 16th century, leading to the formation of countries like the United States and Canada.

Native Americans

Refers to the indigenous peoples of the Americas, present before the arrival of European explorers and settlers.

Pontiac's Uprising

A rebellion led by the Ottawa leader Pontiac in 1763, uniting Native American tribes against British post-colonial policies in the Great Lakes region.

Ohio Country

A term used in the 18th century for the territory west of the Appalachian Mountains, contested by French, British, and various Native American tribes before becoming part of the United States.