Uniform convergence disprove

Question

Why the sequence of functions $f_n(x)=\frac{1}{nx+1}$ is not uniform convergent in (0,1)? I've already prove the pointwise convergence but I can't justify why this sequence is no uniform convergent.

Answer 1

HINT:

What happens when we take $x=1/n\in (0,1)$?

Answer 2

These functions are uniformly convergent on $(\epsilon, 1)$ for any $\epsilon > 0$ but not on the whole interval $(0,1)$.