Binomial Theorem And Its Simple Applications Question 169
Question: The sum of the last eight coefficients in the expansion of $ {{(1+x)}^{15}} $ is
Options:
A) $ 2^{16} $
B) $ 2^{15} $
C) $ 2^{14} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- We have $ ^{15}C_0+{{,}^{15}}C_1+…+{{,}^{15}}C_{15}=2^{15} $
$ \Rightarrow ,2{{(}^{15}}C_8+{{,}^{15}}C_9+…+{{,}^{15}}C_{15})=2^{15} $
$ (\because ,{{,}^{n}}C_{r}={{,}^{n}}{C_{n-r}}) $
therefore $ ^{15}C_8+{{,}^{15}}C_9+…+{{,}^{15}}C_{15}=2^{14} $
BETA
