algebra precalculus - Help in summing up this series involving binomial coefficients?

Find the sum of this series:

$\sum_{r=1}^{19}\left( (-1)^{r-1}\frac{r}{{20\choose r}}\right)$

NOTE: ${20\choose r}$ = $\frac{20!}{(20-r)!r!}$

The final answer is 10/11.
I do have a way to solve this, but i find that to be wayy too tedious and long. Please don't use concepts that are above high school level.

Thanks in advance!