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

Step-by-step solution

( 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 ) ( aligned & a ^ n -12 ~b ^ n -12 = 1 6 2^ n -12 3 3^ n -12 3 =6⁻¹ & n -12=-3 n =9 aligned )