Use Mathematical Induction to Prove the Given Statement for All $$1 \cdot 4 + 2 \cdot 7 + 3 \cdot 10 + \ldots + n ( 3 n + 1 ) = n ( n + 1 ) ^ { 2 }$$

question 21

Short Answer

Use mathematical induction to prove the given statement for all positive integers n.
- $$1 \cdot 4 + 2 \cdot 7 + 3 \cdot 10 + \ldots + n ( 3 n + 1 ) = n ( n + 1 ) ^ { 2 }$$

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Definitions:

Legalized Abortion

The legal provision that allows for the termination of a pregnancy under certain conditions, varying widely by jurisdiction.

Liberals

Individuals or groups advocating for policies that emphasize the need for the government to solve problems, especially those related to social inequality, civil rights, and social justice.

Conservatives

A political ideology favoring the preservation of traditional institutions and values combined with a cautious approach to change and innovation.

Abortion Rights

The rights of individuals to decide upon and access abortion services, often debated in terms of legal, moral, and health considerations.