(a) Use the binomial expansion to expand $$\[ (4-5 x)^{-\frac{1}{2}} \quad|x|< \frac{4}{5} \]$$ in ascending powers of $$\(x\)$$, up to and including the term in $$\(x^{2}\)$$ giving each coefficient as a fully simplified fraction. (4) $$\[ f(x)=\frac{2+k x}{\sqrt{4-5 x}} \quad \text { where } k \text { is a constant and }|x|< \frac{4}{5} \]$$ Given that the series expansion of $$\(\mathrm{f}(x)\)$$, in ascending powers of $$\(x\)$$, is $$\[ 1+\frac{3}{10} x+m x^{2}+\ldots \quad \text { where } m \text { is a constant } \]$$ (b) find the value of $$\(k\)$$, (2) (c) find the value of $$\(m\)$$. (2)

Answer:

Knowledge points:

Solution: