The value of 2 + 1 2 + 1 2 + ........... is - Vidyadip

MCQ

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

A
$1 - \sqrt 2 $
✓
$1 + \sqrt 2 $
C
$1 \pm \sqrt 2 $
D
None of these

✓

Answer

Correct option: B.

$1 + \sqrt 2 $

b
(b) Let $x = 2 + \frac{1}{{2 + \frac{1}{{2 + .....\infty }}}}$

==> $x = 2 + \frac{1}{x}$ (on simplification)

==> $x = 1 \pm \sqrt 2 $

But the value of the given expression cannot be negative or less than $2$, therefore $1 + \sqrt 2 $ is required answer.

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