Question

If $x=\frac{1}{8}$ , find the greatest term in the expansion of ${(1-5x)}^{\frac{-2}{7}}$

• A. 1st
• B. 2nd
• C. 3rd
• D. 4th

Answer 1

The correct option is A 1st

Here, the greatest term in the expansion of ${(1-ax)}^n$ is the greatest integer function of $\left[\frac{n+1}{1+\left|\frac{1}{ax}\right|}\right]$

So, here the greatest term is $\left[\frac{\frac{-2}{7}+1}{1+\left|\frac{8}{5}\right|}\right]=\left[\frac{\frac{5}{7}}{\frac{13}{5}}\right]=1$