Challenging +1.2 This AEA question requires algebraic manipulation and binomial expansion of (1-x²)^(-1/2), but follows a standard pattern with clear guidance. Part (a) is routine algebra, and part (b) is a straightforward application of the binomial theorem to the rearranged form, requiring careful coefficient calculation but no novel insight.
1.(a)Show that \(\sqrt { \frac { 1 + x } { 1 - x } }\) can be written in the form \(\frac { 1 + x } { \sqrt { 1 - x ^ { 2 } } }\) for \(| x | < 1\)
(b)Hence,or otherwise,find the expansion,in ascending powers of \(x\) up to and including the term in \(x ^ { 5 }\) ,of \(\sqrt { \frac { 1 + x } { 1 - x } }\)
1.(a)Show that $\sqrt { \frac { 1 + x } { 1 - x } }$ can be written in the form $\frac { 1 + x } { \sqrt { 1 - x ^ { 2 } } }$ for $| x | < 1$\\
(b)Hence,or otherwise,find the expansion,in ascending powers of $x$ up to and including the term in $x ^ { 5 }$ ,of $\sqrt { \frac { 1 + x } { 1 - x } }$
\hfill \mbox{\textit{Edexcel AEA 2018 Q1 [5]}}