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

question 191

Essay

Find a power series representation for the function $f ( x ) = \frac { 1 - x } { 1 + x }$ and give its interval of convergence.

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Definitions:

Amniocentesis

A medical procedure used in prenatal diagnosis, involving the extraction of a small amount of amniotic fluid surrounding the fetus using a needle through the abdominal wall, to test for genetic disorders and other conditions.

Amniotic Fluid

The fluid surrounding a fetus within the amniotic sac, providing protection and facilitating the exchange of nutrients, water, and biochemical products between mother and fetus.

Lab Testing

The analysis of bodily fluids, tissues, or other substances in a controlled environment to diagnose disease, measure progress, or guide treatment.

Chorionic Villus

Tiny, finger-like projections found in the placenta, involved in nutrient exchange between mother and fetus.