AP EAMCET · Maths · Binomial Theorem
To find the coefficient of \(x^4\) in the expansion of \(\frac{3 x}{(x-2)(x-1)}\), the interval in which the expansion isvalid, is
- A \(-2 < x < \infty\)
- B \(-\frac{1}{2} < x < \frac{1}{2}\)
- C \(-1 < x < 1\)
- D \(-\infty < x < \infty\)
Answer & Solution
Correct Answer
(C) \(-1 < x < 1\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{3 x}{(x-2)(x-1)}\) can be written as \(\frac{6}{x-2}-\frac{3}{x-1}\) \(\begin{aligned} & \therefore \frac{3 x}{(x-2)(x-1)}=\frac{6}{x-2}-\frac{3}{x-1} \\ & =6(x-2)^{-1}-3(x-1)^{-1} \\ & =-3\left(1-\frac{x}{2}\right)+3(x-1)^{-1} \end{aligned}\) It is valid iff…
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