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:

Attachment Theory

A theory focused on how early relationships with caregivers shape an individual's long-term emotional development, specifically how they form and maintain close relationships.

Object Relations Theories

A group of theories in psychoanalysis that focus on the relationships between individuals and the external and internal objects in their environment, considering how these relationships affect emotions and behavior.

Attachment Theories

A group of theories in psychology that describe the dynamics of long-term and short-term interpersonal relationships between humans.

Separation Anxiety

A disorder typically seen in children, characterized by excessive fear and worry about being parted from those to whom the child is attached.