Find the Taylor Series Expansion for F(x) = $\frac { x } { 1 - x }$

question 54

Multiple Choice

Find the Taylor series expansion for f(x) = $\frac { x } { 1 - x }$ and use it to determine which of the following is false?

• A) \(\frac { x } { 1 - x }\) = x + \(x ^ { 2 }\) + \(x ^ { 3 }\) + \(x ^ { 4 }\) +...
• B) \(\frac { 1 } { 2 }\) = \(\frac { 1 } { 3 }\) + \(\left( \frac { 1 } { 3 } \right) ^ { 2 }\) + \(\left( \frac { 1 } { 3 } \right) ^ { 3 }\) + ...
• C) - \(\frac { 1 } { 3 }\) = \(\left( - \frac { 1 } { 2 } \right)\) + \(\left( - \frac { 1 } { 2 } \right) ^ { 2 }\) + \(\left( - \frac { 1 } { 2 } \right) ^ { 3 }\) + ...
• D) - \(\frac { 3 } { 5 }\) = \(\left( \frac { 3 } { 2 } \right)\) + \(\left( \frac { 3 } { 2 } \right) ^ { 2 }\) + \(\left( \frac { 3 } { 2 } \right) ^ { 3 }\) +...
• E) All the statements are true.

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Definitions:

Statement Form

The form or structure of a statement or proposition in logic, usually presented in a symbolic language.

Particular

In logic, refers to propositions or statements that affirm or deny something about only some members of a class, as opposed to universality which concerns all members.

Negative

Expressing denial, disagreement, or the absence of certain characteristics or conditions.

Business Majors

College or university students specializing in fields of study related to business, such as finance, marketing, or management.