AP EAMCET · Maths · Sequences and Series
\(4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}}=\)
- A \((2+\sqrt{5}),(2-\sqrt{5})\)
- B \(2+\sqrt{5}\)
- C \(2-\sqrt{5}\)
- D \(2+\sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(2+\sqrt{5}\)
Step-by-step Solution
Detailed explanation
Let, \(x=4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \ldots . \infty}}}\) \(\begin{aligned} & \Rightarrow x=4+\frac{1}{x} \Rightarrow x^2-4 x-1=0 \\ & \Rightarrow x=2 \pm \sqrt{5} \end{aligned}\) \(\Rightarrow x=2+\sqrt{5}\) and \(x \neq 2-\sqrt{5}\) (It is negative).
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