Find All Values Of $p$ For Which the Series $\sum _ { n = 1 } ^ { \infty } \frac { \ln \left( n ^ { 9 } \right) } { n ^ { p } }$

question 35

Multiple Choice

Find all values of $p$ for which the series $\sum _ { n = 1 } ^ { \infty } \frac { \ln \left( n ^ { 9 } \right) } { n ^ { p } }$ converges.

• A) \(p < 9\)
• B) \(p < 1\)
• C) \(p > 9\)
• D) \(p > 1\)

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Definitions:

Odd Number

An integer that cannot be divided evenly by two, exemplified by numbers like 1, 3, 5, etc.

Mirror

A reflective surface, typically glass coated with a metal amalgam, that reflects a clear image.

Classical View

A traditional perspective or theory in a specific field that has stood the test of time and forms the foundation for subsequent developments.

Triangle

A polygon with three edges and three vertices, representing the simplest form of a polygonal shape.