Binomial Theorem And Its Simple Applications Question 161
Question: If n is an integer greater than 1, then $ a{{-}^{n}}C_1(a-1){{+}^{n}}C_2(a-2)+….+{{(-1)}^{n}}(a-n)= $
[IIT 1972]
Options:
A) $ a $
B) 0
C) $ a^{2} $
D) $ 2^{n} $
Show Answer
Answer:
Correct Answer: B
Solution:
- L.H.S. = $ a[C_0-C_1+C_2-C_3+…{{(-1)}^{n}}.C_{n}] $ $ +[C_1-2C_2+3C_3-….+{{(-1)}^{n-1}}n.C_{n}] $
$ =a.0+0=0 $
BETA
