Further Pure Math 9-1 4PM1: The binomial series Topical Past Paper Questions

Expand $ \left(1-\frac{x}{4}\right)^{-2} $ in ascending powers of x up to and including the term in $ x^{3} $ Where appropriate, express each coefficient as an exact fraction in its lowest term

(a) Show that $$ \frac{a}{\sqrt{4+bx}}=\frac{a}{2}\bigg(1+\frac{bx}{4}\bigg)^{\frac{1}{2}}\text{where}a\text{and}b\text{are positive integers}. $$ The expansion of $ \frac{a}{\sqrt{4+bx}} $ in ascending powers of x can be written as $$ P+Qx+Rx^{2}+Sx^{3} $$ where $P$, $Q$, $R$ an…

(a) Expand $ \left(1 + \frac{x}{3}\right)^{-3} $ in ascending powers of x up to and including the term in $ x^{3} $ Where appropriate express each coefficient as an exact fraction in its lowest terms (b) Write down the range of values of x for which your expression is valid. \beg…