Question 7 - A-Level Maths

Exam Board	OCR MEI
Module	C4 (Core Mathematics 4)
Topic	Generalised Binomial Theorem
Type	Factoring out constants first

Show that \(\frac { 1 } { \sqrt { 25 - x } } = \frac { 1 } { 5 } \left( 1 - \frac { x } { 25 } \right) ^ { - \frac { 1 } { 2 } }\).
Hence expand \(\frac { 1 } { \sqrt { 25 - x } }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\).
Write down the range of values of \(x\) for which the expansion is valid.