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