Disprove uniform convergence of $\sum_{n=1}^{\infty} \frac{x}{(1+x)^n}$ in $[0,\infty)$ How would I show that $\sum_{n=1}^{\infty} \frac{x}{(1+x)^n}$ does not uniformly converge in $[0,\infty)$? 
I don't know how to approach this problem.
Thank you.

$$ \sup_{x \in [0,\infty)} \sum_{n=m}^{2m} \frac{x}{(1+x)^n}  \geq \sup_{x \in [0,\infty)}  \frac{mx}{(1+x)^{2m}}  \geq  \frac{mx}{(1+x)^{2m}} \bigg|_{x=1/m} = \frac1{(1+ \frac{1}{m} )^{2m}}\to \frac1{e^2}.$$
Thus the series is not uniformly Cauchy on $[0,\infty).$
