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If the coefficient of x7 and x8 in the expansion of 2 x... | (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

If the co-efficient of x⁷ and x⁸ in the expansion of

{\left( {2 + {x \over 3}} \right)^n}

are equal, then the value of n is equal to _____________.

Explanation

${}^n{C_7}{2^{n - 7}}{1 \over {{3^7}}} = {}^n{C_8}{2^{n - 8}}{1 \over {{3^8}}}$ $\\ \Rightarrow n - 7 = 48$ $\\ \Rightarrow n = 55$

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