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

question 36

Essay

Use mathematical induction to prove the following inequality for all $n \geq 2$ .
$$\frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 4 } } + \frac { 1 } { \sqrt { 6 } } + \ldots + \frac { 1 } { \sqrt { 2 n } } > \frac { \sqrt { n } } { \sqrt { 2 } }$$

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Definitions:

Framing

The process of constructing and presenting information or issues in a specific way that influences how they are perceived and interpreted.

Robert Entman

A scholar known for his contributions to the field of communication studies, particularly in framing and media effects.

Agenda-setting Theory

Agenda-setting theory posits that media doesn't tell us what to think, but what to think about, by selecting the issues that receive extensive coverage, thus influencing the public's perception of what topics are important.

McCombs and Shaw

Researchers known for establishing the Agenda-Setting Theory, which suggests that media has a significant influence on what topics the public perceives as important.