Time until completion for $n$-th order reaction

For an $n$-th order reaction, how to determine the time until all the reactants run out?


My approach is the following. The reaction kinetics is modeled by the differential equation


$$\frac{\mathrm d[A]}{\mathrm dt}= - k{[A]^n}$$


where $n$ is the reaction order, which can take values in the nonnegative integers and even in the rational and negative numbers. Suppose we have a chemical reaction similar to the following one


$$\ce{A -> B}$$ 


In this problem, I'll take an example $5$ equation with similar form with the equation above, and different order $n$. Assuming the $n$ value of the $5$ example is $1,2,0,-1$ and $\frac{1}{2}$, we will get these equations for the five example after we input the $n$ value and integrate the kinetic differential equation.


(reaction with 1st order) $\ln[A] = -kt + \ln[A]\_0 $


(reaction with 2nd order) $\frac{1}{[A]} = \frac{1}{[A]\_0} +kt$


(reaction with 0th order) $[A] = [A]\_0 -kt$


(reaction with $\frac{1}{2}$ order) $2\left(\sqrt {[A]} - \sqrt {[A]\_0}\right) = -kt$


(reaction with $-1$ order) $\frac{1}{2}[A]^2 = -kt + \frac{1}{2}\left([A]\_0\right)^2$


what I was thinking is, if I want to determine the time until the reaction complete, then I will have to define $t$ when $[A]=0$ (note: I will call the time that needed to complete the reaction $t\_\text{complete}$) which is not defined for reaction with 1st and 2nd order because it will involve $\infty$ value, in fact as much as I know, $t\_\text{complete}$ will not be defined for $n \ge 1$, but we can calculate $t\_\text{complete}$ for $n \lt 1$. 


so for 0th order, the $t\_\text{complete} = \frac{[A]\_0}{k}$


for $\frac{1}{2}$ order, $t\_\text{complete} = \frac{2\sqrt{[A]\_0}}{k}$


for $-1$ order, $t\_\text{complete} = \frac{([A]\_0)^2}{2k}$.


my question. is all the reaction with $n \ge 1$ never complete? and is all the reaction with $n \lt 1$ is the only reaction that can complete?
and I know what I've done is just manipulating the rate law equation, but if this is correct, can the $t\_\text{complete}$ that I got above determine the time that needed for order $n \lt 1$ to complete?


