Use Mathematical Induction to Prove the Formula for Every Positive $$+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$$

question 18

Essay

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $$+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$$

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Definitions:

Normally Distributed Populations

Populations in which the variables of interest follow a distribution that conforms to the properties of a normal curve, implying a symmetric distribution of data around the mean.

Independent Samples

Two or more groups of data that are collected from separate and unrelated populations, with each group not influencing the others.

Degrees of Freedom

How many separate values or measures could be allocated to a statistical distribution.

Unequal-variances T-test

A statistical test used for comparing the means of two groups that do not have the same variance.