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is there a general identity for $$\sum_{r=1}^n \frac{r}{{n \choose r}} $$

My Approach

I tried to write $\frac{1}{{n \choose r}}$ as $$\frac{n+1}{{n+2}} \sum_{r=1}^n \frac{1}{{n+1 \choose r+1}}+ \frac{1}{{n+1 \choose r}} $$ but couldn't get any further as I wasn't able to make a telescopic sum which would cancel out.

0 Answers0