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Question Number 130449 by Dwaipayan Shikari last updated on 25/Jan/21

(1/((2−(√3))^3 ))−(1/((2+(√3))^3 ))+(1/((6−(√3))^3 ))−(1/((6+(√3))^3 ))+(1/((10−(√3))^3 ))−(1/((10+(√3))^3 ))+..

$$\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+\frac{\mathrm{1}}{\left(\mathrm{6}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{6}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+\frac{\mathrm{1}}{\left(\mathrm{10}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{10}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+.. \\ $$

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