Given that the expansion of ${{\left( 1-\frac{x}{2} \right)}^{n}}(3-x)=a-13x+5b{{x}^{2}}+\ldots $,

Question

Given that the expansion of ${{\left( 1-\frac{x}{2} \right)}^{n}}(3-x)=a-13x+5b{{x}^{2}}+\ldots $, find the values of $n$, $a$ and $b$.

Accepted Answer

$n=8,\ a=3,\ b=5$

Binomial Theorem - Coefficients in Products of Binomial Expansions