Q. In the expansion of ${(1 + x)}^{50}$, the sum of the coefficients of odd powers of $x$ is
A) 0
B) $2^{49}$
C) $2^{50}$
D) $2^{51}$
Explanation
(b)
We have, ${(1 + x)}^{50} = \sum_{r = 0}^{50}{\ ^{50}C_{r}x^{r}}$. (The sum of coefficients of odd powers of $x$)
$= \ ^{50}C_{1} + \ ^{50}C_{3} + ... + \ ^{50}C_{49}$
$= 2^{50 - 1} = 2^{49}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.