Question

The coefficient of $\frac{a_{1}}{a_{1} + a_{2}} + \frac{a_{3}}{a_{3} + a_{4}}$ in the expansion of $\frac{a_{2}}{a_{2} + a_{3}}$ is.

• A. $\frac{2a_{3}}{a_{2} + a_{3}}$
• B. $(5^{1/2} + 7^{1/6})^{642}$
• C. $(2 + \sqrt{2})^{4}$
• D. $(183!) + 3^{183}$

Answer 1

Answer: (A)

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

Answer 2

$x^{3}$

∴ $\left( x - \frac{1}{x} \right)^{7}(1 + x)^{m}(1 - x)^{n}$

Now putting $x^{2}$

⇒ $x^{m}$ ⇒ $\left( x + \frac{1}{x^{2}} \right)^{2n},$

$x^{m}$Coefficient of $\frac{(2n)!}{(m)!(2n - m)!}$.