Find the Terms of the Maclaurin Series For $\frac { 1 } { \sqrt { 1 - x } }$

question 28

Multiple Choice

Find the terms of the Maclaurin series for $\frac { 1 } { \sqrt { 1 - x } }$ , as far as the term in $x ^ { 3 }$ .

• A) \(1 - x + x ^ { 2 } - x ^ { 3 }\)
• B) \(1 - \frac { 1 } { 2 } x + \frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 8 } x ^ { 3 }\)
• C) \(1 + \frac { 1 } { 2 } x + \frac { 3 } { 8 } x ^ { 2 } + \frac { 5 } { 16 } x ^ { 3 }\)
• D) \(1 - \frac { 1 } { 2 } x + \frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 8 } x ^ { 3 }\)
• E) \(1 + \frac { 1 } { 2 } x + \frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 }\)
• F) \(1 - \frac { 1 } { 2 } x + \frac { 1 } { 6 } x ^ { 2 } + \frac { 1 } { 24 } x ^ { 3 }\)
• G) \(1 + \frac { 1 } { 2 } x + \frac { 3 } { 4 } x ^ { 2 } + \frac { 15 } { 16 } x ^ { 3 }\)
• H) \(1 - \frac { 1 } { 2 } x + \frac { 3 } { 8 } x ^ { 2 } + \frac { 7 } { 24 } x ^ { 3 }\)

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