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

question 87

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$\sum _ { i = 1 } ^ { n } 96 i ^ { 5 } = 8 n ^ { 2 } ( n + 1 ) ^ { 2 } \left( 2 n ^ { 2 } + 2 n - 1 \right)$

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Definitions:

External Genitalia

The outer parts of the reproductive system visible on the body's exterior, varying between males and females.

Phenylalanine

An essential amino acid that is a building block of proteins and is necessary for the body's production of neurotransmitters.

Genetically Inherited

Traits or conditions that are passed from parents to their offspring through genes.