WBJEE · Maths · Sequences and Series
The value of \(\mathrm{n}\) for which \(\frac{\mathrm{x}^{\mathrm{n}+1}+\mathrm{y}^{\mathrm{n}+1}}{\mathrm{x}^{\mathrm{n}}+\mathrm{y}^{\mathrm{n}}}\) is the geometric mean of \(\mathrm{x}\) and \(\mathrm{y}\) is
- A \(\mathrm{n}=-\frac{1}{2}\)
- B \(\mathrm{n}=\frac{1}{2}\)
- C \(\mathrm{n}=1\)
- D \(\mathrm{n}=-1\)
Answer & Solution
Correct Answer
(A) \(\mathrm{n}=-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Hints: \(\frac{x^{n+1}+y^{n+1}}{x^n+y^n}=\sqrt{x y} \Rightarrow x^{n+1}+y^{n+1}=\sqrt{x y}\left(x^n+y^n\right)\)…
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