AP EAMCET · Maths · Binomial Theorem
If the middle term in the expansion of \((1+x)^{2 n}\) is the greatest term, then \(x\) lies in the interval
- A \(\left(\frac{n}{n+1}, \frac{n+1}{n}\right)\)
- B \(\left(\frac{n+1}{n}, \frac{n}{n+1}\right)\)
- C \((n-2, n)\)
- D \((n-1, n)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{n}{n+1}, \frac{n+1}{n}\right)\)
Step-by-step Solution
Detailed explanation
In the expansion of \((1+x)^{2 n}\), middle term is \({ }^{2 n} \mathrm{C}_n x^n\). Since, middle term is the greatest term. \(\therefore{ }^{2 n} \mathrm{C}_n x^n>{ }^{2 n} \mathrm{C}_{n-1} x^{n-1}\) \(\text { and }{ }^{2 n} \mathrm{C}_r x^n>{ }^{2 n} \mathrm{C}_{n+1} x^{n+1}\)…
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