Why is the following series uniformly convergent:$$\sum_{n=1}^{\infty }(-1)^{n+1}\frac{1}{n}.e^{-nx}$$? where $ x\geq 0$
I tried the Weierstrass-M test, but it doesn't work here because:$\left | (-1)^{n+1}\frac{1}{n}.e^{-nx} \right |= \frac{1}{n}.e^{-nx}\leq \frac{1}{n}$, and $ \sum_{n=1}^{\infty }\frac{1}{n}$ is divergent.