Show that
C_{0} - C_{1}\left(\frac{1+x}{1+nx} \right)+C_{2}\left( \frac{1+2x}{(1+nx)^{2}}\right)-C_{3}\left(\frac{1+3x}{(1+nx)^{3}} \right)+ ......... =0
-
UP 0 DOWN 0 0 1
1 Answers
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
