- #1
amind
- 36
- 4
Homework Statement
If $$a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}}$$
Find $$\sum_{r=0}^{n} \frac{r}{\binom{n}{r}}$$ in terms of an and n
2. The attempt at a solution
Let $$f(x) =\sum_{r=0}^{n} \frac{x^r}{\binom{n}{r}}$$
Then, an = f(1).
Observe that f'(1) is the required sum.
I was thinking if I could find an expression for f(x) then I could obtain the required sum, but with no luck.
Other than that I've tried expressing the binomial coefficients in terms of factorials, again in vain. So I am looking for some pointers that don't involve finding an by using Taylor series like I found on Google.