$\frac{1}{n}/\frac{1}{n^2}$ understanding The limit of $\frac{1}{n}/\frac{1}{n^2}$ when $n \rightarrow +\infty$ is $+\infty$. 

By calculation this is an obvious result, yet I don't understand why this is true. 
$1/n$ will never reached the value $0$ because the équation $1/n=0$ hasn't any solutions. It's exactly the same for $1/n^2$.
Moreover the difference $1/n-1/n^2=0$ when $n \rightarrow +\infty$. 
So why $\frac{1}{n}/\frac{1}{n^2} \ne 1$ when $n\rightarrow +\infty$.
It's all about the speed of convergence. Clearly $\lim_{n\rightarrow \infty}\frac{1}{n}=0$ and $\lim_{n\rightarrow \infty}\frac{1}{n^2}=0$, but $\frac{1}{n^2}$ tends to zero faster than $\frac{1}{n}$.

Thus when we consider the ratio $\frac{1}{n}/\frac{1}{n^2}$ the denominator will then to zero faster than the nominator. Indeed, just pick a large value for $n$ and compare: $n=10$ yields $\frac{1}{n}=\frac{1}{10}$ and $\frac{1}{n^2}=\frac{1}{100}$.

In many such cases you can use l'Hopitals rule, and if you think about it, all this rule does is compare the speed of convergences of the nominator to that of the denominator.
Adding to EdMo38, take examples of n getting smaller and smaller, eg. n=1 : lim=1, n=0.1 : lim=10, n=0.01 : lim=100, n=0.001 : lim=1000, etc.