Q. The sum of the last eight coefficient in the expansion of ${(1 + x)}^{15}$ is
A) $2^{16}$
B) $2^{15}$
C) $2^{14}$
D) None of these
Explanation
(c)
We know that,
$\ ^{15}C_{0} + \ ^{15}C_{1} + \ ^{15}C_{2} + \ldots + \ ^{15}C_{15} = 2^{15}$
$\Longrightarrow 2\left( \ ^{15}C_{8} + \ ^{15}C_{9} + \ldots + \ ^{15}C_{15} \right)2^{15}\ \ \left\lbrack \because\ ^{n}C_{r} = \ ^{n}C_{n - r} \right\rbrack$
$\Longrightarrow \ ^{15}C_{8} + \ ^{15}C_{9} + \ldots + \ ^{15}C_{15} = 2^{14}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.