Use the Binomial Series to Expand $( 4 + x ) ^ { 3 / 2 }$

question 325

Essay

Use the binomial series to expand $( 4 + x ) ^ { 3 / 2 }$ as a power series. State the radius of convergence.

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Definitions:

Sexually Transmitted Infections

Infections that are primarily spread through sexual contact; they can also be transferred by blood, needles, or from mother to child.

Common Bacterial STI

Refers to sexually transmitted infections caused by bacteria that are prevalent among sexually active individuals, such as chlamydia, gonorrhea, and syphilis.

Infectious Disease

Illnesses caused by pathogenic microorganisms, such as bacteria, viruses, fungi, or parasites, which can be transmitted, directly or indirectly, from one person to another.

Chlamydia

A common sexually transmitted infection (STI) caused by the bacterium Chlamydia trachomatis, which can affect both men and women.