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

question 52

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:

Dependent Variable

A variable in an experiment or study whose changes are determined by the presence or manipulation of one or more independent variables.

Independent Variable

A variable in statistical analysis that is manipulated or categorized to observe its effect on a dependent variable.

Standard Deviation

A measure that is used to quantify the amount of variation or dispersion of a set of data values.

Covariance

A measure indicating the extent to which two random variables change together.