Use Mathematical Induction to Prove That $$3 \mid \left( n ^ { 3 } + 3 n ^ { 2 } + 2 n \right) \text { for all } n \geq 1$$

question 34

Essay

Use mathematical induction to prove that $$3 \mid \left( n ^ { 3 } + 3 n ^ { 2 } + 2 n \right) \text { for all } n \geq 1$$

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Definitions:

Urinary Excretion

The process of removing waste and toxic substances from the body through the formation and discharge of urine.

Respiration

Physiological processes that collectively supply animal cells with oxygen and dispose of their waste carbon dioxide.

Antidiuretic Hormone

A hormone that helps to control the balance of water in the body by reducing the amount of water excreted by the kidneys.

Distal Tubule

Part of the nephron in the kidney responsible for the reabsorption of ions, water, and nutrients.