Find the Radius of Convergence of the Series $$\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 3 } x ^ { n } } { 2 ^ { n } }$$

question 38

Short Answer

Find the radius of convergence of the series.
$$\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 3 } x ^ { n } } { 2 ^ { n } }$$

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Definitions:

Psychoactive Drugs

Substances that affect the mind, mood, and perceptions by altering the functioning of the brain.

Neuroadaptive

Neuroadaptive refers to changes and adaptations in the nervous system in response to various stimuli, experiences, or injuries, aiming at maintaining or restoring function.

Disinhibiting

Reducing or removing inhibitions, leading to a decrease in the control over impulses and behavior.

Dehydrating

The process of removing moisture or water content from a substance, often resulting in preservation or concentration.