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Question Number 64785 by Rio Michael last updated on 21/Jul/19

Answered by LPM last updated on 21/Jul/19

$$1){\mathrm{x}}_{\mathrm{n}}⩽2,\mathrm{\forall }\mathrm{n}⩾1$$$$2){\mathrm{x}}_{\mathrm{n}}⩽{\mathrm{x}}_{\mathrm{n}+1},\mathrm{\forall }\mathrm{n}⩾1$$$$\Rightarrow {\mathrm{x}}_{\mathrm{n}}\mathrm{cov}$$$$\mathrm{let}{\mathrm{x}}_{\mathrm{n}}\to \mathrm{L}\Rightarrow {\mathrm{L}}^2-2\mathrm{L}=0$$$$\Rightarrow \mathrm{L}=0\mathrm{or}\mathrm{L}=2$$$$\Rightarrow \mathrm{L}=2({\mathrm{x}}_{\mathrm{n}}>0)$$$${\log }_{\mathrm{e}}{\mathrm{x}}_{\mathrm{n}}\to {\log }_{\mathrm{e}}2$$

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