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

question 53

Essay

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

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Definitions:

Average Starting Salary

The mean initial compensation that individuals receive when they start a new job, typically used as a benchmark in job offer negotiations.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values differ from the mean.

Normally Distributed

A descriptor for a type of statistical distribution that is symmetric around its mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Average Starting Salary

The median initial compensation received by employees in their first position post-graduation or certification.