Binomial Theorem And Its Simple Applications Question 156
Question: $ C_0-C_1+C_2-C_3+…..+{{(-1)}^{n}}C_{n} $ is equal to
[MNR 1991; RPET 1995; UPSEAT 2000]
Options:
A) $ 2^{n} $
B) $ 2^{n}-1 $
C) 0
D) $ {2^{n-1}} $
Show Answer
Answer:
Correct Answer: C
Solution:
- We know that $ {{(1+x)}^{n}}={{,}^{n}}C_0+{{,}^{n}}C_1x+{{,}^{n}}C_2x^{2}+….+{{,}^{n}}C_{n}x^{n} $
Putting x = -1, we get $ {{(1-1)}^{n}}={{,}^{n}}C_0-{{,}^{n}}C_1+{{,}^{n}}C_2-…..{{(-1)}^{nn}}C_{n} $
Therefore $ C_0-C_1+{C_{2}}-C_3+….(-1){{,}^{n}}C_{n}=0 $
BETA
