AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^{50}\) in the expansion of \((\mathrm{l}+x)^{1000}+x(\mathrm{l}+x)^{999}\) \(+x^2(1+x)^{998}+\ldots+x^{1000}\) is
- A \({ }^{1000} C_{50}\)
- B \({ }^{999} \mathrm{C}_{50}\)
- C \({ }^{1000} C_{51}\)
- D \({ }^{1001} C_{50}\)
Answer & Solution
Correct Answer
(D) \({ }^{1001} C_{50}\)
Step-by-step Solution
Detailed explanation
Expression given is, \(\begin{aligned} & f(x)=(l+x)^{1000}+x(l+x)^{999}+x^2(l+x)^{998} +\ldots \ldots .+x^{1000}, \end{aligned}\) This is a Geometric progression, common ratio \(=\frac{x}{1+x}\) and number of terms 1001 . So,…
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