If the coefficients of x^7 & x^8 in the e | vedclass

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Question

$2^n {\left( {1\,\, + \,\,\frac{x}{6}} \right)^n} $

$\Rightarrow T_{r + 1} = 2^n . ^nC_r {\left( {\frac{x}{6}} \right)^r}$

$\Rightarro

Vedclass · Accepted Answer

$55$

Vedclass · Answer

$2^n {\left( {1\,\, + \,\,\frac{x}{6}} \right)^n} $

$\Rightarrow T_{r + 1} = 2^n . ^nC_r {\left( {\frac{x}{6}} \right)^r}$

$\Rightarrow 2^n . ^nC_7 . \frac{1}{{{6^7}}} = 2^n $. $^nC_8 .\frac{1}{{{6^8}}} $

$\Rightarrow 6 . ^nC_7 = ^nC_8 $

$\Rightarrow\,\, n - 7 = 48$

$ \Rightarrow n = 55$

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

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