Q. $The\ coefficient\ of\ \ 1/x\ \ in\ the\ expansion\ of\ \left( \frac{1}{x} + 1 \right)^{n}({1 + x)}^{n}\ is$
A) $\ \ ^{2n}C_{n}$
B) $\ ^{2n}C_{n - 1}\$
C) $\ ^{2n}C_{1}\$
D) $\ ^{n}C_{n - 1}$
Explanation
(b)
$\left( \frac{1}{x} + 1 \right)^{n}({1 + x)}^{n} = \frac{1}{x^{n}}(1 + x)^{2n}$
$\ \ \ \ \ \ \ \ = \frac{1}{x^{n}}\left( 1 + \ ^{2n}C_{1}x + \ ^{2n}C_{2}x^{2} + \ldots + \ ^{2n}C_{n - 1}x^{n - 1} + \ldots + \ ^{2n}C_{2n}x^{2n} \right)$
$The\ coefficient\ of\frac{1}{x}\ is\ \ ^{2n}C_{n - 1}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.