Question 50

If x = $$\frac{1}{2 + \frac{1}{2 +\frac{1}{2 + .....\infty} }}$$ then x =

Solution

From the given question we can say that,

$$x=\frac{1\ }{2+x}\left(as\ the\ series\ reapeted\ from\ the\ same\ position\right).$$

or,$$x^2+2x=1.$$

or,$$x^2+2x-1=0.$$

or,$$x^2+2x+1-2=0.$$

or,$$\left(x+1\right)^2=2.$$

or,$$x+1=\sqrt{2\ }.$$

or,$$x=\left(\sqrt{2\ }-1\right).$$

So, C is correct choice.

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