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

question 104

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$\sum _ { i = 1 } ^ { n } 36 i ^ { 5 } = 3 n ^ { 2 } ( n + 1 ) ^ { 2 } \left( 2 n ^ { 2 } + 2 n - 1 \right)$

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Definitions:

Personality Psychology

Area of psychology in which the psychologists study the differences in personality among people.

Trait Perspective

A psychological viewpoint that emphasizes the description and measurement of consistent personality characteristics, or traits, as the primary means of understanding individual differences.

Other Perspectives

Other perspectives involve considering alternative viewpoints or approaches to understanding concepts, problems, or situations.

Temperament

The behavioral characteristics that are fairly well established at birth, such as “easy,” “difficult,” and “slow to warm up”; the enduring characteristics with which each person is born.