Find the first three terms, in ascending powers of \(x\), of the binomial expansion of
$$( 1 + x ) ^ { - \frac { 1 } { 2 } }$$
9
A student substitutes \(x = 2\) into the expansion of \(( 1 + x ) ^ { - \frac { 1 } { 2 } }\) to find an approximation for \(\frac { 1 } { \sqrt { 3 } }\)
Explain the mistake in the student's approach. [0pt]
[1 mark]
9
By substituting \(x = - \frac { 1 } { 4 }\) in your expansion for \(( 1 + x ) ^ { - \frac { 1 } { 2 } }\) find an approximation for \(\frac { 1 } { \sqrt { 3 } }\) Give your answer to three significant figures.