Q. The coefficient of $x$ in the expansion of $(1 + x)(1 + 2x)(1 + 3x)\ldots\ldots(1 + 100x)$ is
A) 5050
B) 10100
C) 5151
D) 4950
Explanation
(a)
The coefficient of $x$ in the expansion of
$(1 + x)(1 + 2x)(1 + 3x)$…$(1 + 100x)$
$= 1 + 2 + 3 +$….$+ 100$
$\frac{100(100 + 1)}{2} = 50 \times 101 = 5050$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.