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