If $a_{1}, a_{2}, a_{3}, a_{4}$ are the coefficients of 2^nd, 3^rd, 4^th and 5^th terms respectively in ${(1 + x)}^{n}$ then $\frac{a_{1}}{a_{1} + a_{2}} + \frac{a_{3}}{a_{3} + a_{4}} =$

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$\frac{a_{2}}{a_{2} + a_{3}}$

$\frac{2 a_{2}}{a_{2} + a_{3}}$

$\frac{a_{3}}{a_{2} + a_{3}}$

$\frac{2 a_{3}}{a_{2} + a_{3}}$

answer is B.

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Detailed Solution

$\frac{a_{1}}{a_{1} + a_{2}} + \frac{a_{3}}{a_{3} + a_{4}} = \frac{^{n} C_{1}}{^{(n + 1)} C_{2}} + \frac{^{n} C_{3}}{^{(n + 1)} C_{4}}$

$\frac{n! \times 2}{(n + 1) n!} + \frac{n (n - 1) (n - 2)}{3!} \times \frac{4 \times 3!}{(n + 1) n (n - 1) (n - 2)}$

$= \frac{2}{n + 1} + \frac{4}{n + 1}$

$= \frac{6}{n + 1}$

$= 2. \frac{a_{2}}{a_{2} + a_{3}}$

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