# Asteroid sum

**Calculus**Level 4

\[\displaystyle \lim_{n\to\infty } \sum_{r=0}^{n} \dfrac{r^{2}}{n^{\frac{9}{2}}}\sqrt{n^{3} - r^{3}}\]

If the summation above can be expressed in the form \(\dfrac{a}{b}\), where \(a,b\) are co-prime natural numbers, then find the value of \(a + b + (a\times b\)).