First slide

Theory of equations

Question

$The value of 2 + \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + \dots \dots \infty}}} is$

Easy

A

$2 + \sqrt{2}$
B

$1 + \sqrt{2}$
C

3
D

3.2

Solution

Let the given expression be equal to x.
$\begin{array}{l} Then x = 2 + \frac{1}{x} \Rightarrow x^{2} - 2 x - 1 = 0 \\ \Rightarrow x = \frac{2 \pm \sqrt{4 + 4}}{2} = 1 \pm \sqrt{2} \end{array}$
$But, the given expression is positive. Therefore, x = 1 + \sqrt{2}$
$is the value of the given expression.$

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