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Question-177131




Question Number 177131 by mokys last updated on 01/Oct/22
Commented by Frix last updated on 02/Oct/22
(((1/(1×2))+(1/(3×4))+...+(1/((2n−1)×2n)))/((1/((n+1)×2n))+(1/((n+2)×(2n−1)))+...+(1/((n+n)×(2n−(n−1))))))=((3n+1)/2)
$$\frac{\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}+…+\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)×\mathrm{2}{n}}}{\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)×\mathrm{2}{n}}+\frac{\mathrm{1}}{\left({n}+\mathrm{2}\right)×\left(\mathrm{2}{n}−\mathrm{1}\right)}+…+\frac{\mathrm{1}}{\left({n}+{n}\right)×\left(\mathrm{2}{n}−\left({n}−\mathrm{1}\right)\right)}}=\frac{\mathrm{3}{n}+\mathrm{1}}{\mathrm{2}} \\ $$

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