Sequence And Series Question 451
Question: In the expansion of $ \frac{a+bx}{e^{x}} $ , the coefficient of $ x^{r} $ is
Options:
A) $ \frac{a-b}{r,!} $
B) $ \frac{a-br}{r,!} $
C) $ {{(-1)}^{r}}\frac{a-br}{r,!} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ (a+bx){e^{-x}} $ $ =(a+bx){ 1-\frac{x}{1\ !}+\frac{x^{2}}{2\ !}-\frac{x^{3}}{3\ !}+…….+{{(-1)}^{n}}\frac{x^{n}}{n\ !}+…… } $ The coefficient of $ x^{r} $ $ =a\frac{{{(-1)}^{r}}}{r\ !}+b\frac{{{(-1)}^{r-1}}}{(r-1)\ !}=\frac{{{(-1)}^{r}}}{r\ !}(a-br) $ .
BETA
