$If\ the\ second\ term\ in\ the\ expansion\left\lbrack \sqrt[13]{a} + \frac{a}{\sqrt{a^{- 1}}} \right\rbrack^{n}\$is$\ {14a}^{5/2},\ then\ the\ value\ of\ \frac{n_{C_{3}}}{n_{C_{2}}}\ is$

Question

Dr. Abubacker · Accepted Answer

(a)
We have , $T_{2} = 14a^{5/2}$
$\Longrightarrow \ ^{n}C_{1}(a^{1/13})^{n - 1}(a^{3/2})^{1} = 14a^{5/2}$
$\Longrightarrow \ {na}^{\frac{n - 1}{13} + \frac{3}{2}} = 14a^{5/2}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 14$
$	herefore\frac{\ ^{n}C_{3}}{\ ^{n}C_{2}} = \frac{\ ^{14}C_{3}}{\ ^{14}C_{2}} = 4$

Q. $If\ the\ second\ term\ in\ the\ expansion\left\lbrack \sqrt[13]{a} + \frac{a}{\sqrt{a^{- 1}}} \right\rbrack^{n}\$is$\ {14a}^{5/2},\ then\ the\ value\ of\ \frac{n_{C_{3}}}{n_{C_{2}}}\ is$

Explanation

Reviewed by Dr. Abubacker

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