Question

If the number of terms in the expansion ${(1-\frac{2}{x}+\frac{4}{x^2})}^n$ $x\ne 0$,is 28,then the sum of the coefficients of all the terms in this expansion is

• A. $2187$
• B. $243$
• C. $729$
• D. $64$

Answer 1

Answer: (C)

$729$

If the expression in the question is ${\left(1-\frac{2}{x}+\frac{4}{x^2}\right)}^n$

Then number of terms would be

$\begin{array}{c}\frac{\left(n+1\right)\left(n+2\right)}{1.2}=28\\ \left(n+1\right)\left(n+2\right)=56\end{array}$

This gives $n=6$

And sum of coefficient would be ${\left(1-2+4\right)}^6=729$

Hence, option $C$ is correct answer.