# Closed form of generating function

Find the closed form of the generating function of the sequence $\frac{{n \choose r}}{n^r \cdot (r+3)}$ where $n$ tends to infinity. I tried to make a sort of infinite gp to use infinite gp sum formula but I failed......

• Hint: $$\left(1+\frac{x}{n}\right)^n = \sum_{r=0}^n \binom{n}{r} \frac{x^r}{n^r} \quad\text{ and }\quad \int_0^1 x^{r+2} dx = \frac{1}{r+3}$$ – achille hui Mar 30 '15 at 17:26
• Thank you very much! This helped me in successfully finding the generating function! – Manan Mar 31 '15 at 15:28