Mathematics - Limits Question with Solution | TestHub

Since ${\tan }^{-1}\frac{1+2r}{1+r^2(r+1{)}^2}={\tan }^{-1}(r+1{)}^2-{\tan }^{-1}{r}^2$, the sum telescopes to ${\tan }^{-1}(n+1{)}^2-\pi /4$. Its limit is $\pi /4$, whose tangent is 1.