How do I evalutate the lim n->infinity of: (n+1)/n^2
Since it will tend to $\displaystyle \frac{\infty}{\infty}$, you can use L'Hospital's rule...
$\displaystyle \lim_{n \to \infty}\frac{n + 1}{n^2} = \lim_{n \to \infty}\frac{\frac{d}{dx}(n + 1)}{\frac{d}{dx}(n^2)}$
$\displaystyle = \lim_{n \to \infty}\frac{1}{2n}$
$\displaystyle = 0$.
Alternatively, just divide numerator by denominator...
$\displaystyle \lim_{n \to \infty}\frac{n + 1}{n^2} = \lim_{n \to \infty}\frac{1}{n} + \frac{1}{n^2}$
$\displaystyle = 0 + 0$
$\displaystyle = 0$.