AP EAMCET · Maths · Binomial Theorem
\(|x| \lt 1\), the coefficients of \(x^2\) in the power series expansion of \(\frac{x^4}{(x+1)(x-2)}\) is
- A 3
- B 0
- C -1
- D -3
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{x^4}{(x+1)(x-2)}=\frac{x^4}{3}\left[\frac{1}{(x-2)}-\frac{1}{(x+1)}\right] \\ & =\frac{x^4}{3}\left[\frac{-1}{2}(1-x)^{-1}-(1+x)^{-1}\right]\end{aligned}\)…
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