Question

If the coefficients of $x^7$ & $x^8$ in the expansion of ${[2+\frac{x}{3}]}^n$ are equal then the value of n is

• A. $15$
• B. $45$
• C. $55$
• D. $56$

Answer 1

The correct option is C $55$

Hence

$T_8=T_9$

${}^n{C}_8{2}^{n-8}{3}^{-8}={}^n{C}_7{2}^{n-7}{3}^{-7}$

${}^n{C}_8=6{}^n{C}_7.$

$\frac{n!}{(n-8)!.8!}=6.\frac{n!}{(n-7)!.7!}$

$n-7=6.8$

$n-7=48$

$n=55$.