1Check if i'm wrong anywhere..
\sum_{r=0}^{n}{(-1)^{r}} C^{n}_{r} \frac{1+rx}{(1+nx)^{r}}
= \sum_{r=0}^{n}{(-1)^{r}}\ C^{n}_{r} \frac{1}{(1+nx)^{r}} + \sum_{r=0}^{n}{(-1)^{r}}\frac{n}{r} C^{n-1}_{r-1} \frac{rx}{(1+nx)^{r}}
Solving further...we get,
(1-\frac{1}{1+nx})^{n}-\frac{nx}{1+nx}(1-\frac{1}{1+nx})^{n-1}
Which gives,
(\frac{nx}{1+nx})^{n}-(\frac{nx}{1+nx})^{n}=0
I skipped a step
