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

question 139

Short Answer

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

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Definitions:

Depolarized

A state in which sodium ions flow to the inside of the cell membrane, making the outside less positive. Depolarization occurs when a neuron responds to stimuli such as heat, pressure, or chemicals.

Nerve Impulse

Electrochemical messages transmitted from neurons to other neurons and effectors.

Cerebrum

The biggest section of the brain, which is in charge of voluntary muscle movement, sight, speech, taste, auditory processing, cognition, and memory.

Lumbar Puncture

A medical procedure where a needle is inserted into the lower part of the spinal column to collect cerebrospinal fluid, used for diagnostic purposes.