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Question

Question: In the expansion of \(\frac{a + bx}{e^{x}}\), the coefficient of \(x^{r}\) is....

In the expansion of a+bxex\frac{a + bx}{e^{x}}, the coefficient of xrx^{r} is.

A

abr!\frac{a - b}{r!}

B

abrr!\frac{a - br}{r!}

C

(1)rabrr!( - 1)^{r}\frac{a - br}{r!}

D

None of these

Answer

(1)rabrr!( - 1)^{r}\frac{a - br}{r!}

Explanation

Solution

12+13.123+15.125+.....\frac{1}{2} + \frac{1}{3}.\frac{1}{2^{3}} + \frac{1}{5}.\frac{1}{2^{5}} + .....\infty

loge32\log_{e}\sqrt{\frac{3}{2}}

The coefficient of

xrx ^ { r } loge12\log_{e}\sqrt{\frac{1}{2}}.