Question

Find the greatest term of the following expansion :
$(5-4x{)}^{-7}$ when $x=\frac{1}{2}$

Answer 1

$\Rightarrow 5^{-7}{(1-\frac{4x}{5})}^{-7}$

$\Rightarrow r<\frac{x(n-1)}{1-x}=\frac{\frac{4}{5}\times \frac{1}{2}\left(6\right)}{1-\frac{4}{10}}=\frac{\frac{4}{10}\times 6}{\frac{6}{10}}$

$r<4$ (an integer)

$\therefore$ Two great terms are present.

$T_4$ and $T_5$

$T_4{=}^9{C}_3{\left(\frac{4}{10}\right)}^3\times \frac{1}{5^7},T_5{=}^{10}{C}_4{\left(\frac{4}{10}\right)}^4\times \frac{1}{5^7}$