A sequence $\left\{ {{x}_{n}} \right\}$ of positive numbers is defined as \({{x}_{n\,+1}}=\fr

Question

A sequence $\left\{ {{x}_{n}} \right\}$ of positive numbers is defined as ${{x}_{n\,+1}}=\frac{{{x}_{n}}^{2}+2}{2{{x}_{n}}+3}$ for $n\in {{\mathbb{Z}}^{+}}$. The sequence $\left\{ {{x}_{n}} \right\}$ converges to a number $\lambda $ as $n$ tends to infinity. Find the value of $\lambda $ exactly.[2]

Accepted Answer

(a) $\lambda=\frac{-3+\sqrt{17}}{2}$

2007 SRJC P1 Q4

2007 SRJC P1 Q4

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