Binomial Theorem And Its Simple Applications Question 180
Question: In the expansion of $ {{(1+x)}^{50}}, $ the sum of the coefficient of odd powers of x is
[UPSEAT 2001; Pb. CET 2004]
Options:
A) 0
B) $ 2^{49} $
C) $ 2^{50} $
D) $ 2^{51} $
Show Answer
Answer:
Correct Answer: B
Solution:
- We have, $ {{(1+x)}^{50}}=\sum\limits_{r=0}^{50}{{}^{50}C_{r}x^{r}} $ .
Therefore, sum of coefficients of odd power of x = $ {}^{50}C_1+{}^{50}C_3+…+{}^{50}C_{49} $ = $ \frac{1}{2}[{}^{50}C_0+{}^{50}C_1+…+{}^{50}C_{50}]=\frac{1}{2}[2^{50}]=2^{49} $ .
BETA
