Find a Power Series Representation for the Function $f ( x ) = \ln \sqrt { 1 - x }$

question 204

Essay

Find a power series representation for the function $f ( x ) = \ln \sqrt { 1 - x }$ and determine the radius of convergence.

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Definitions:

Light Waves

Electromagnetic waves that are visible to the human eye, responsible for the phenomenon of light.

Perceived Color

refers to the color an observer sees in various conditions, which can differ from the physical color due to lighting and context.

Depth Cue

Visual information that helps perceive the distance or three-dimensional characteristics of an object, scene, or spatial layout.

Interposition

A visual cue for depth perception where one object partially blocks the view of another, indicating that the blocking object is closer to the viewer.