I am currently studying for an Analysis exam and I have come across this problem in a textbook:
Study the simple and uniform convergence of this sequence of functions in $(0,\infty)$. $$f_n(x)=\frac{nx}{1+n^2x^2}$$
I was going to first check the simple convergence by taking the limit of $f_n(x)$, which is $\lim_{n\to\infty} \frac{nx}{1+n^2x^2}$ when $x>0$, but in my textbook, it says that for $x>0$, $f_n(x)=\frac{\frac{1}{nx}}{1+\frac{1}{n^2x^2}}$.
Can anybody help me figure out why the parts with the $x$ variable are inverted?