Use the Binomial Series to Expand $\sqrt [ 3 ] { 1 + x ^ { 2 } }$

question 270

Essay

Use the binomial series to expand $\sqrt [ 3 ] { 1 + x ^ { 2 } }$ as a power series. State the radius of convergence.

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Definitions:

Capillary Bed

Networks of small blood vessels that facilitate the exchange of materials (such as oxygen and carbon dioxide) between the blood and tissues.

Sweat Gland

A specialized epidermal structure involved in the production of sweat, playing a key role in body temperature regulation.

Thymus Gland

A gland located in the chest that is part of the immune system, involved in the development of T lymphocytes.

Parathyroid Gland

Small glands located in the neck behind the thyroid that regulate calcium levels in the blood and bone metabolism.