Q. If $n$ is an integer greater than 1, then $a - \ ^{n}C_{1}(a - 1) + \ ^{n}C_{2}(a - 2) + ... + ({- 1)}^{n}(a - n)$ is equal to
A) $a$
B) 0
C) $a^{2}$
D) $2^{n}$
Explanation
(b)
$a\lbrack C_{0} - C_{1} + C_{2} - C_{3} + \ldots({- 1)}^{n} \bullet C_{n}\rbrack$
$+ \lbrack C_{1} - 2C_{2} + 3C_{3} - \ldots + ( - 1)^{n - 1}nC_{n}\rbrack$
$= a0 + 0 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.