Limit Question

**jzellt** · December 12th 2009, 10:00 PM

How do I evalutate the lim n->infinity of: (n+1)/n^2

**Prove It** · December 12th 2009, 10:02 PM

Originally Posted by jzellt

How do I evalutate the lim n->infinity of: (n+1)/n^2

Since it will tend to $\frac{\infty}{\infty}$ , you can use L'Hospital's rule...

$\lim_{n \to \infty}\frac{n + 1}{n^2} = \lim_{n \to \infty}\frac{\frac{d}{dx}(n + 1)}{\frac{d}{dx}(n^2)}$

$= \lim_{n \to \infty}\frac{1}{2n}$

$= 0$ .

Alternatively, just divide numerator by denominator...

$\lim_{n \to \infty}\frac{n + 1}{n^2} = \lim_{n \to \infty}\frac{1}{n} + \frac{1}{n^2}$

$= 0 + 0$

$= 0$ .

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