AP EAMCET · Maths · Binomial Theorem
For \(|x| < \frac{1}{5}\), the coefficient of \(x^3\) in the expansion of \(\frac{1}{(1-5 x)(1-4 x)}\) is
- A 369
- B 370
- C 371
- D 372
Answer & Solution
Correct Answer
(A) 369
Step-by-step Solution
Detailed explanation
\(|x| < \frac{1}{5}\) and \(\frac{1}{(1-5 x)(1-4 x)}\) \(=(1-5 x)^{-1} \cdot(1-4 x)^{-1}\) then by binomial expansion \(=\left\{1+5 x+25 x^2+125 x^3+\ldots\right\}\) \(\cdot\left\{1+4 x+16 x^2+64 x^3+\ldots\right\}\) the coefficient of \(x^3\) in this expansion is…
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