1. [SOLVED] riemann sum question

Hi, long-time lurker, first time poster

The problem is this: find the limit of Sum[(i^2/(n^3 + i^3))] (going from i=1 to n) as n approaches infinity. Sorry I don't know how to write fancy math text but basically it's the limit of a series going to n as n --> infinity.

I figure it's probably a riemann sum question, but I tend to have difficulty with those. Any help would be nice

2. $\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{i=1}^{n}{\frac{i^{2}}{n^{3}+i^{3} }}=\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\sum\limits_{i=1}^{n}{\left( \frac{i}{n} \right)^{2}\cdot \frac{1}{1+\left( \frac{i}{n} \right)^{3}}},$

thus $\int_{0}^{1}{\frac{x^{2}}{1+x^{3}}\,dx}$ is the limit and the partition is $\Delta x_{i}=\frac{1-0}{n}=\frac{1}{n}.$