Binomial Theorem And Its Simple Applications Question 40
Question: The coefficient of $ x^{m} $ in $ {{(1+x)}^{m}}+{{(1+x)}^{m+1}}+……+{{(1+x)}^{n}},m\le n $ is
Options:
A) $ ^{n+1}{C_{m+1}} $
B) $ ^{n-1}{C_{m-1}} $
C) $ ^{n}C_{m} $
D) $ ^{n}{C_{m+1}} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ ^{m}C_{m}+{{,}^{m+1}}C_{m}+…..+{{,}^{n}}C_{m} $
$ {{=}^{m+1}}{C_{m+1}}+{{,}^{m+1}}C_{m}+…..+{{,}^{n}}C_{m} $
$ {{=}^{m+2}}{C_{m+1}}+{{,}^{m+2}}C_{m}+…..+{{,}^{n}}C_{m} $
$ ={{,}^{n}}{C_{m+1}}+{{,}^{n}}C_{m}={{,}^{n+1}}{C_{m+1}} $
BETA
