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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......

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

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