Prove the Inequality for the Indicated Integer Values Of $n$ $\left( \frac { 9 } { 8 } \right) ^ { n } > n , n \geq 29$

question 45

Essay

Prove the inequality for the indicated integer values of $n$ .
$\left( \frac { 9 } { 8 } \right) ^ { n } > n , n \geq 29$

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Definitions:

Cultural Processes

the dynamic mechanisms through which cultures are formed, maintained, and transformed over time, including adaptation, innovation, and communication.

Environmental Adaptation

The process by which organisms adjust to changes in their habitat or environment, often resulting in biological or behavioral changes.

Natural Selection

A fundamental mechanism of evolution, where organisms better adapted to their environment tend to survive and reproduce more successfully.

Speciation

The evolutionary process by which populations evolve to become distinct species, primarily through genetic divergence and reproductive isolation.