Q. In the polynomial $(x - 1)(x - 2)(x - 3)\ldots(x - 100)$. The coefficient of $x^{99}$is
A) 5050
B) $- 5050$
C) 100
D) 99
Explanation
(b)
We have, $(x - 1)(x - 2)(x - 3)\ldots(x - 100)$
Number of terms = 100
$\therefore$ Coefficient of $x^{99}$ in $(x - 1)(x - 2)(x - 3)\ldots(x - 100$)
$= ( - 1 - 2 - 3 - ... - 100)$
$= - (1 + 2 + ... + 100)$
$= - \frac{100 \times 101}{2} = - 5050$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.