Use Mathematical Induction to Prove the Following Inequality for All $n \geq 2$

question 83

Essay

Use mathematical induction to prove the following inequality for all $n \geq 2$ .
$\frac { 1 } { \sqrt { 19 } } + \frac { 1 } { \sqrt { 38 } } + \frac { 1 } { \sqrt { 57 } } + \ldots + \frac { 1 } { \sqrt { 19 n } } > \frac { \sqrt { n } } { \sqrt { 19 } }$

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Definitions:

Runout

A term that describes the maximum deviation or variation of an object from its intended perfect form or the total movement of a rotational part.

Points

Specific locations or positions in space, defined by coordinates in a given reference frame, often with no physical size.

Position

The location or arrangement of something in relation to other entities.

Geometric Tolerance

A type of tolerance that defines the form, orientation, location, and runout of a feature on a part.