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Question Number 108805 by ZiYangLee last updated on 19/Aug/20

$$\mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and}\mathrm{the}\mathrm{common}$$$$\mathrm{ratio}\mathrm{of}\mathrm{a}\mathrm{geometric}\mathrm{sequence}\left\{a_{\mathrm{n}}\right\}\mathrm{be}1$$$$\mathrm{and}r.$$$$\mathrm{If}\left\{a_{\mathrm{n}}\right\}\mathrm{satisfy}\mid a_{\mathrm{n}-1}-a_1\mid ⩽\mid a_{\mathrm{n}}-a_1\mid \mathrm{for}$$$$\mathrm{all}\mathrm{n}⩾2,\mathrm{find}\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{values}\mathrm{of}r.$$

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