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6-6-6-6-6-2-6-6-6-3-6-6-6-1000-6-




Question Number 165309 by cortano1 last updated on 29/Jan/22
 (6/(6+(√6))) + (6/(6^2 +(√6))) +(6/(6^3 +(√6))) +...+(6/(6^(1000) +(√6))) =?
$$\:\frac{\mathrm{6}}{\mathrm{6}+\sqrt{\mathrm{6}}}\:+\:\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{2}} +\sqrt{\mathrm{6}}}\:+\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{3}} +\sqrt{\mathrm{6}}}\:+…+\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{1000}} +\sqrt{\mathrm{6}}}\:=? \\ $$

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