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Question Number 18779 by chux last updated on 29/Jul/17

$$\mathrm{If}\frac{1}{2\mathrm{x}}+\frac{1}{2}(\frac{1}{2\mathrm{x}}+\frac{1}{2}(\frac{1}{2\mathrm{x}}+\frac{1}{2}(\frac{1}{2\mathrm{x}}+......=\mathrm{y}$$$$\mathrm{what}\mathrm{does}\mathrm{x}\mathrm{equals}?$$$$$$$$\mathrm{a})1/2$$$$\mathrm{b})2/4$$$$\mathrm{c})1$$$$\mathrm{d})1/4$$

Commented by chux last updated on 29/Jul/17

$$\mathrm{i}\mathrm{noticed}\mathrm{that}\mathrm{too}\mathrm{when}\mathrm{i}\mathrm{tried}$$$$\mathrm{to}\mathrm{solve}\mathrm{it}.\mathrm{I}\mathrm{was}\mathrm{astonished}\mathrm{when}\mathrm{i}$$$$\mathrm{discovered}\mathrm{that}\mathrm{it}\mathrm{had}\mathrm{options}$$$$\mathrm{which}\mathrm{are}\mathrm{fractions}\mathrm{of}\mathrm{numbers}.$$

Commented by dioph last updated on 29/Jul/17

$$y=\frac{1}{2x}+\frac{1}{2}y$$$$\frac{1}{2}y=\frac{1}{2x}$$$$x=\frac{1}{y},\mathrm{\forall }y\ne 0$$

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