For |x|<1 , the constant term in the expansion of 1(x−1)2(x−2) is k then |2k| is _______

1(x−1)2(x−2)=1(1−x)2(−2)(1−x2) =1−2(x−1)−2(x−2)−1=(1−x)−2(−12)(1−x2)−1=−12 |k|=12⇒|2k|=1

For |x|<1 , the constant term in the expansion of 1(x−1)2(x−2) is k then |2k| is _______

1(x−1)2(x−2)=1(1−x)2(−2)(1−x2) =1−2(x−1)−2(x−2)−1=(1−x)−2(−12)(1−x2)−1=−12 |k|=12⇒|2k|=1

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For $| x | < 1$ , the constant term in the expansion of $\frac{1}{{(x - 1)}^{2} (x - 2)}$ is k then $| 2 k |$ is _______

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\frac{1}{{(x - 1)}^{2} (x - 2)} = \frac{1}{{(1 - x)}^{2} (- 2) (1 - \frac{x}{2})}

$= \frac{1}{- 2} {(x - 1)}^{- 2} {(x - 2)}^{- 1} = {(1 - x)}^{- 2} (- \frac{1}{2}) {(1 - \frac{x}{2})}^{- 1} = - \frac{1}{2}$

$| k | = \frac{1}{2} \Rightarrow | 2 k | = 1$

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For |x|<1 , the constant term in the expansion of 1(x−1)2(x−2) is k then |2k| is _______

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For $| x | < 1$ , the constant term in the expansion of $\frac{1}{{(x - 1)}^{2} (x - 2)}$ is k then $| 2 k |$ is _______