Binomial Theorem And Its Simple Applications Question 130
Question: If the coefficient of the middle term in the expansion of $ {{(1+x)}^{2n+2}} $ is p and the coefficients of middle terms in the expansion of $ {{(1+x)}^{2n+1}} $ are q and r, then
Options:
A) $ p+q=r $
B) $ p+r=q $
C) $ p=q+r $
D) $ p+q+r=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
- Since (n+2)th term is the middle term in the expansion of $ {{(1+x)}^{2n+2}} $ , therefore $ p={{,}^{2n+2}}{C_{n+1}} $ . Since (n+1)th and (n+2)th terms are middle terms in the expansion of (1+x)2n+1, therefore $ q={{,}^{2n+1}}C_{n} $ and $ r={{,}^{2n+1}}{C_{n+1}} $ But $ ^{2n+1}C_{n}+{{,}^{2n+1}}{C_{n+1}}={{,}^{2n+2}}{C_{n+1}} $
$ \therefore ,q+r=p $
BETA
