TS EAMCET · Maths · Binomial Theorem
When \(|x| \lt 2\) coefficient of \(x^2\) in the power series expansion of \(\frac{x}{(x-2)(x-3)}\) is
- A \(\frac{1}{6}\)
- B \(\frac{5}{36}\)
- C \(\frac{25}{216}\)
- D \(\frac{5}{18}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{36}\)
Step-by-step Solution
Detailed explanation
Expansion is \(\frac{x}{(x-2)(x-3)}\) \(\begin{aligned} & =\frac{3}{x-3}-\frac{2}{x-2}=\frac{1}{1-\frac{x}{2}}-\frac{1}{1-\frac{x}{3}} \\ & =\left(1-\frac{x}{2}\right)^{-1}-\left(1-\frac{x}{3}\right)^{-1} \end{aligned}\) For coefficient of \(x^2\)…
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