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AP EAMCET · Maths · Limits

If \(\lim _{n \rightarrow \infty} x_n\) exists and is finite, \(x_1=2, x_{n+1}=\frac{a+b x_n}{b+c x_n} \forall n \in N\) and \(\mathrm{c}>\mathrm{b}>\mathrm{a}>\mathrm{o}\) then \(\lim _{n \rightarrow \infty} x_n=\)

  1. A \(\sqrt{\frac{a b}{c}}\)
  2. B \(\sqrt{\frac{a}{c}}\)
  3. C \(\sqrt{\frac{a}{b}}\)
  4. D \(\sqrt{a / b}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{\frac{a}{c}}\)

Step-by-step Solution

Detailed explanation

\(\therefore \lim _{n \rightarrow \infty} x n\) enirts and fiwite let \(\lim _{n \rightarrow \infty} x n=1\) \(\Rightarrow \mathrm{l}=\frac{\mathrm{a}+\mathrm{bl}}{\mathrm{b}+\mathrm{cl}} \Rightarrow \mathrm{bl}+\mathrm{cl}^2=\mathrm{a}+\mathrm{bl}\)…