WBJEE · Maths · Binomial Theorem
If \(n\) is even posirive integer, then the condition that the greatest term in the expansion of \((a+x)^{n}\) may also have the greatest coefficient, is
- A \(\frac{n}{n+2} < x < \frac{n+2}{n}\)
- B \(\frac{n}{n+1} < x < \frac{n+1}{n}\)
- C \(\frac{n+1}{n+2} < x < \frac{n+2}{n+1}\)
- D \(\frac{n+2}{n+3} < x < \frac{n+3}{n+2}\)
Answer & Solution
Correct Answer
(A) \(\frac{n}{n+2} < x < \frac{n+2}{n}\)
Step-by-step Solution
Detailed explanation
For greatest term of \((1+x)^{n},\) we have \(\quad \frac{n}{2} < \frac{n+1}{1+x} < \frac{n}{2}+1\) \(\Rightarrow \quad \frac{n}{2} < \frac{n+1}{1+x}\) and \(\frac{n+1}{1+x} < \frac{n}{2}+1\) \(\Rightarrow \quad 1+x < \frac{n+1}{n / 2}\) and \(\frac{n+1}{\frac{n}{2}+1} < 1+x\)…
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