Binomial Theorem And Its Simple Applications Question 201
Question: The value of $ ^{20}C_0+{{,}^{20}}C_1+{{,}^{20}}C_2+{{,}^{20}}C_3+{{,}^{20}}C_4 $ $ +{{,}^{20}}C_{12}+{{,}^{20}}C_{13}+{{,}^{20}}C_{14}+{{,}^{20}}C_{15} $ is
Options:
A) $ 2^{19}-\frac{( ^{20}C_{10}+{{,}^{20}}C_9 )}{2} $
B) $ 2^{19}-\frac{( ^{20}C_{10}+,2{{\times }^{20}}C_9 )}{2} $
C) $ 2^{19}-\frac{^{20}C_{10}}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Given series is $ ^{20}C_0+{{,}^{20}}C_1+{{,}^{20}}C_2+…+{{,}^{28}}C_8 $
$ =\frac{(2^{20}-{{,}^{20}}C_{10})}{2}-{{,}^{20}}C_9 $
$ =2^{19}-\frac{({{,}^{20}}C_{10}+2\times {{,}^{20}}C_9)}{2} $
BETA
