JEE Mains · Maths · STD 11 - 8. sequence and series
If \(A=\sum\limits_{n=1}^{\infty} \frac{1}{\left(3+(-1)^{n}\right)^{n}}\) and \(B=\sum\limits_{n=1}^{\infty} \frac{(-1)^{n}}{\left(3+(-1)^{n}\right)^{n}}\), then \(\frac{ A }{ B }\) is equal to:
- A \(\frac{11}{9}\)
- B \(1\)
- C \(-\frac{11}{9}\)
- D \(-\frac{11}{3}\)
Answer & Solution
Correct Answer
(C) \(-\frac{11}{9}\)
Step-by-step Solution
Detailed explanation
\(A=\left(\frac{1}{2}+\frac{1}{4^{2}}+\frac{1}{2^{3}}+\frac{1}{4^{4}}+\ldots \ldots \infty\right)\) \(A=\left(\frac{1}{2}+\frac{1}{2^{3}}+\ldots \infty\right)+\left(\frac{1}{4^{2}}+\frac{1}{4^{4}}+\ldots \ldots \infty\right)\)…
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