Use Mathematical Induction to Prove the Following for Every Positive $n$

question 30

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$1 + 3 + 9 + 27 + \ldots + 3 ^ { n - 1 } = \frac { 3 ^ { n } - 1 } { 2 }$

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Definitions:

Sociology

The scientific study of society, including patterns of social relationships, social interaction, and culture, to understand human behavior and social structures.

Androcentric World

A perspective or practice that places male human beings or the masculine point of view at the center of one's view of the world and its culture and history.

Marxism

A sociopolitical and economic ideology based on the theories of Karl Marx, focusing on class struggle, the conflict between the bourgeoisie (capitalist class) and the proletariat (working class), and advocating for a classless society.

Forces Of Production

The physical and intellectual resources a society has with which to make a living.