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Use Mathematical Induction to Prove the Following Inequality for All n2n \geq 2

question 12

Essay

Use mathematical induction to prove the following inequality for all n2n \geq 2 .
123+146+169++123n>n23\frac { 1 } { \sqrt { 23 } } + \frac { 1 } { \sqrt { 46 } } + \frac { 1 } { \sqrt { 69 } } + \ldots + \frac { 1 } { \sqrt { 23 n } } > \frac { \sqrt { n } } { \sqrt { 23 } }

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Definitions:

Skull

The bone structure that forms the head in vertebrates, supports the structures of the face, and protects the brain.

Pelvic Region

The lower part of the torso, situated between the abdomen and the legs, which encompasses the pelvis.

Joint

A structure in the body where two or more bones meet, allowing for movement and support.

Structure

A composition or arrangement of parts or elements forming a complex or coherent whole.

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