Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of (24 + (1)/(34)) ^ n , in the increasing powers of (1)/(34) be 64 : 1 . If the sixth term from the beginning

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The ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of ${\left(24 + \dfrac{1}{34}\right)}^{n} in the increasing powers of$ \dfrac{1}{34} $be$ 64 : 1 $Now according to given data we have,$ \dfrac{{T}_{5}}{{T}_{n - 3}} = \dfrac{C4 n {\left({2}^{1 / 4}\right)}^{n - 4}{\left({3}^{- 1 / 4}\right)}^{4}}{Cn - 4 n {\left({2}^{1 / 4}\right)}^{4}{\left({3}^{- 1 / 4}\right)}^{n - 4}} = \dfrac{64}{1} $$ ⇒ 2\dfrac{n - 8}{4}3\dfrac{n - 8}{4} = {6}^{1 / 4} $$ ⇒ {6}^{n - 8} = 6 $$ ⇒ n - 8 = 1 ⇒ n = 9 $So,$ {T}_{6} = C5 9 {\left({2}^{1 / 4}\right)}^{4}{\left({3}^{- 1 / 4}\right)}^{5} = \dfrac{84}{34} $Now comparing with$ {T}_{6} = \dfrac{\alpha}{34} $,We get$ \alpha = 84

Let the ratio of the fifth term from the beginning to the fifth...

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