Binomial Theorem And Its Simple Applications Question 171
Question: If $ {{(1+x)}^{n}}=C_0+C_1x+C_2x^{2}+….+C_{n}x^{n} $ , then the value of $ C_0+2C_1+3C_2+….+(n+1)C_{n} $ will be
[MP PET 1996; RPET 1997; DCE 1995; AMU 1995; EAMCET 2001; IIT 1971]
Options:
A) $ (n+2){2^{n-1}} $
B) $ (n+1)2^{n} $
C) $ (n+1){2^{n-1}} $
D) $ (n+2)2^{n} $
Show Answer
Answer:
Correct Answer: A
Solution:
- Trick: Put n=1, the expression is equivalent to $ ^{1}C_0+{{2.}^{1}}C_1=1+2=3 $ Only option (a) gives the value.
BETA
