In the binomial ( 2 1/3 + 3 − 1/3 ) n , if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is 1/6 , then n equal to

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T r + 1 ​ = n C r ​ a n − r ⋅ b r where a = 2 1/3 and b = 3 − 1/3 T 7 ​ from beginning = n C 6 ​ a n − 6 b 6 and T 7 ​ from end = n C 6 ​ b n − 6 a 6 ​ ⇒ b n − 12 a n − 12 ​ = 6 1 ​ ⇒ 2 3 n − 12 ​ ⋅ 3 3 n − 12 ​ = 6 − 1 ⇒ n − 12 = − 3 ⇒ n = 9 ​

Mathematics - Binomial Theorem Question with Solution | TestHub

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