Discussion Forum

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

Answer:

Explanation:

Clearly  number of terms in the expansion of $(1-\frac{2}{x}-\frac{4}{x^{2}})^{n}$  is  $\frac{(n+2((n+1)}{2} or ^{n+2}C_{2}$   { Assuming $\frac{1}{x}$ $\frac{1}{x^{2}}$ are distinct }

$\frac{(n+2)(n+1)}{2}=28$

$\Rightarrow n=0$

$\Rightarrow (n+2)(n+1)=56=(6+1)(6+2)$

= n=6

 Hence sum of coefficeints

    $(1-2+4)^{6}=3^{6}=729$

  NOTE:   As $\frac{1}{x}$ $\frac{1}{x^{2}}$ are function of same variables , therefore number of disimilar  terms will be 2n+1 . ie. odd, which is not possible . Hence it contaibns error