Binomial Theorem And Its Simple Applications Question 143
Question: $ ^{n}C_0-\frac{1}{2}{{,}^{n}}C_1+\frac{1}{3}{{,}^{n}}C_2-……+{{(-1)} ^{n}}\frac{^{n}C_{n}}{n+1}= $
Options:
A) n
B) 1/n
C) $ \frac{1}{n+1} $
D) $ \frac{1}{n-1} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Trick: Put $ n= $ 1, 2
At $ n=1,{{,}^{1}}C_0-\frac{1}{2}{{,}^{1}}C_1=1-\frac{1}{2}=\frac{1}{2} $
At $ n=2,,{{,}^{2}}C_0-\frac{1}{2},{{,}^{2}}C_1+\frac{1}{3}{{,}^{2}}C_2=1-1+\frac{1}{3}=\frac{1}{3} $ which is given by option C.
BETA
