Use Mathematical Induction to Prove the Statement Is True for All

question 128

Essay

Use mathematical induction to prove the statement is true for all positive integers n.
- $$\text { The integer } n ^ { 3 } + 2 n \text { is divisible by } 3 \text { for every positive integer } n \text {. }$$

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Definitions:

High-Side

In electrical systems, refers to the part of a circuit that is at a higher potential relative to a common ground.

Low-Side

Refers to the part of a circuit or system that is at a lower electrical potential compared to other parts, often used in reference to switches or power converters.

Low-Pressure Liquid

A liquid that is at a lower pressure than its surrounding environment, often used in contexts like refrigeration and hydraulic systems.

Low-Pressure Gas

Gas at a pressure lower than the atmospheric pressure, often used in various industrial and commercial applications for its specific properties.