Binomial Theorem And Its Simple Applications Question 28
Question: If $ x+y=1 $ , then $ \sum\limits_{r=0}^{n}{r^{n}C_{r}x^{r}{y^{n-r}}} $ equals
Options:
A) 1
B) n
C) nx
D) ny
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] We have, $ \sum\limits_{r=0}^{n}{r{{,}^{n}}C_{r}x^{r},{y^{n-r}}=\sum\limits_{r=0}^{n}{r\frac{n}{r}{{,}^{n-1}}{C_{r-1}}{x^{r-1}}x^{1}{y^{n-r}}}} $
$ =nx\sum\limits_{r=0}^{n}{^{n-1}{C_{r-1}}{x^{r-1}}{y^{(n-1)-(r-1)}}} $
$ =nx{{(x+y)}^{n-1}}=nx,[\because x+y=1] $
BETA
