[tex]\lim\limits_{n\to \infty}\left(\dfrac{n+1}{n}\right)\dfrac{n^2+1}{n} =\\ \\ = \lim\limits_{n\to \infty}\dfrac{n+1}{n}\cdot \lim\limits_{n\to \infty}\dfrac{n^2+1}{n} \\ \\ = 1\cdot \infty\\ \\ = \infty[/tex]
