Question

The coefficient of $(7.995)^{1/3}$ in the following expansion $|x| < 1$is.

• A. $\left( \frac{2x}{1 + x} \right)^{n}$
• B. $\left( \frac{1 + x}{2x} \right)^{n}$
• C. $\left( \frac{1 - x}{1 + x} \right)^{n}$
• D. $1 + n\left( 1 - \frac{1}{x} \right) + \frac{n(n + 1)}{2!}\text{ }\left( 1 - \frac{1}{x} \right)^{2} + .....\infty,$

Answer 1

Answer: (C)

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

Answer 2

The given sigma is expansion of

$10^{2} + 3 \times 4^{4} + 5$.

∴ $(\sqrt{2} + 1)^{6} - (\sqrt{2} - 1)^{6} =$will occur in $70\sqrt{2}$.

$140\sqrt{2}$

∴ Coefficient is – ¹⁰⁰C₅₃.