Find the sum when n=1000. Show all your steps. Use the properties of summation.
i=1 -->n ((4i/n^2)+(i^3/n))*(6/i)
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You're performing this sum, then?
$\displaystyle \displaystyle\sum_{i=1}^{n}\left[\left(\frac{4i}{n^{2}}+\frac{i^{3}}{n}\right)\frac {6}{i}\right]?$
If so, I would note two things:
1. You can simplify a bit before summing.
2. It's true from principles of induction that
$\displaystyle \displaystyle\sum_{i=1}^{n}i^{2}=\frac{n(n+1)(2n+1 )}{6}.$
So what does that tell you?