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