The values of $x$ for which $\frac{x}{(x-1)^2(x-2)}$ has an expansion and the coefficient of $x^n$ in such…

The values of $x$ for which $\frac{x}{(x-1)^2(x-2)}$ has an expansion and the coefficient of $x^n$ in such expansion are respectively
  1. $|x| < 1,1-n-\frac{1}{2^n}$
  2. $|x| < 2,1-n-\frac{1}{2^n}$
  3. $|x| < 1,0$
  4. $x \in \mathbb{R}, 1-n-\frac{1}{2^n}$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2017 (25 Apr Shift 2)

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