If the second term of the expansion `[a^(1/(13))+a/(sqrt(a^(-1)))]^n` is `14 a^(5//2)` , then the value of `(^n C_3)/(^n C_2)` is.

Answer

4

Explanation

`T_(2) = .^(n)C_(1) (a^(1//13))^(n-1).asqrt(a)= 14a^(5//2)`
or `n.a^((n-1)/(13)) = 14a`
or `n.a^((n-14)/(13)) = 14`
or `(n-14)/(13) = 0`
or `n = 14`
`rArr (.^(14)C_(3))/(.^(14)C_(2)) = (14!)/(3!.11!) (2!12!)/(14!) = 12/3 = 4`