If the coefficients of $x^7$ and $x^8$ in $\displaystyle \left ( 2 + \frac{x}{3} \right )^n$ are equal then n $=$

Coefficient of $x^7 = coefficient of </span><span>$x^8

$\Rightarrow \displaystyle \frac{2^n \cdot ^nC_7}{6^7} = 2^n \cdot \frac{^n C_8}{6^8}$

$\Rightarrow 6 (^nC_7)=^nC_8$

$\Rightarrow 6 \cdot \displaystyle \frac{n!}{(n-7)!7!}=\frac{n!}{(n-8!)8!}$

$\Rightarrow \displaystyle \frac{6}{n-7}=\frac{1}{8} \Rightarrow n-7 =48$

$\Rightarrow n = 55$