Sendo dado $$\ln \left(2\sqrt{4}\sqrt[3]{6}\sqrt[4]{8}\dots \sqrt[n]{2n}\right)=a_n\text{e}\ln \left(\sqrt{2}\sqrt[3]{3}\sqrt[4]{4}\dots \sqrt[2n]{2n}\right)=b_n$$ então, $$\frac{\ln 2}{2}-\frac{\ln 3}{3}+\frac{\ln 4}{4}-\frac{\ln 5}{5}+\dots +\frac{\ln 2n}{2n}$$ é igual a: