Question 4 - A-Level Maths

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2005
Session	June
Topic	Generalised Binomial Theorem
Type	Substitute expression for variable

Find the binomial expansion of \(( 1 + x ) ^ { - \frac { 1 } { 2 } }\) up to the term in \(x ^ { 2 }\).
Hence, or otherwise, obtain the binomial expansion of \(\frac { 1 } { \sqrt { 1 + 2 x } }\) up to the term in \(x ^ { 2 }\), in simplified form.
Use your answer to part (b) with \(x = - 0.1\) to show that \(\sqrt { 5 } \approx 2.23\).