# 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 $$a + b + (a\times b$$).