The coefficient of x in the expansion of $(1 - a x)^{- 1} (1 - b x)^{- 1} (1 - c x)^{- 1}$ is?

a + b + c

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a - b - c

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- a + b + c

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a - b + c

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Solution

The correct option is C $a + b + c$
${(1 - a x)}^{- 1} = 1 + {^{- 1} C}_{1} (- a x) + \frac{(- 1) (- 2)}{2!} (- a x)^{2}$
We can get coefficient of $x$ by taking $x$ from one bracket and $1$ from remaining.
$∴$ Coefficient of $x = (a) . (1) . (1)$
$+ (1) . (b) . (1)$
$+ (1) . (1) . (c)$
$= a + b + c .$
Hence the answer is $a + b + c .$

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The coefficient of x in the expansion of (1−ax)−1(1−bx)−1(1−cx)−1 is?

The correct option is C a+b+c(1−ax)−1=1+−1C1(−ax)+(−1)(−2)2!(−ax)2We can get coefficient of x by takingx from one bracket and 1 from remaining.∴ Coefficient of x=(a).(1).(1) +(1).(b).(1) +(1).(1).(c)=a+b+c.Hence the answer is a+b+c.

The coefficient of x in the expansion of $(1 - a x)^{- 1} (1 - b x)^{- 1} (1 - c x)^{- 1}$ is?