Question

If the coefficients of $x^7$ and $x^8$ in are equal, then $n$ is equal to

Answer 1

It is given, coefficient of $x^7=$ Coefficient of $x^8$
${}^n{C}_7^{2n–7}{\left(\frac{1}{3}\right)}^7{=}^n{C}_8{2}^{n–8}{\left(\frac{1}{3}\right)}^8$
$\Rightarrow 6{(}^n{C}_7){=}^n{C}_8$
$\Rightarrow 48=n–7$
$\Rightarrow n=55$