Q. The coefficient of $x^{n}$ in the expansion of $(1 + 2x + {3x}^{2} + .\ldots)^{1/2}$ is
A) $- 1$
B) 0
C) 2
D) 1
Explanation
(d)
$(1 + 2x + {3x}^{2} + ...)^{1/2} = {\lbrack(1 - x)}^{- 2}\rbrack^{1/2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (1 - x)^{- 1}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ = 1 + x + x^{2} + \ldots + x^{n} + \ldots\infty$
$\therefore$The coefficient of $x^{n} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.