Prove the Following Statement by Mathematical Induction $3+7+11+\cdots+(4 n-1)=n(2 n+1)$

question 24

Essay

Prove the following statement by mathematical induction: $3+7+11+\cdots+(4 n-1)=n(2 n+1)$

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Definitions:

Regression Method

A statistical technique used to analyze relationships between variables and predict outcomes.

Industrial Lathe Sales

The commercial activity involving the selling of lathes, which are machine tools used for shaping materials, within the industrial market.

Regression Equation

An algebraic representation of the regression line, describing the relationship between the dependent and independent variables.

Regression Method

A statistical technique used to model and analyze the relationships between variables and how one variable's change affects another.