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:

Edward VII

King of the United Kingdom and the British Dominions, and Emperor of India, from 1901 to 1910, known for modernizing the British Home Fleet and his role in the Entente Cordiale.

Condition Subsequent

A condition subsequent is a condition in a contract that, when met, terminates an existing obligation under the contract, as opposed to initiating it.

Breach Of Contract

The failure to perform any term of a contract, written or oral, without a legitimate legal excuse.

Cause Of Action

A cause of action is a set of facts sufficient to justify a right to sue to obtain money, property, or the enforcement of a right against another party.