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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