Please help me express the following sum (click to see) in closed form.

Question

babyslapmafro · Answer

$$\sum_{k=1}^{n-1}\frac{ 5k^3 }{ 3n^2 }$$

slaaibak · Answer

I can give you a few pointers:  The 5/3n^2 is a constant, so you can write it before the sigma sign.  Then, sum up to n and subtract the n'th term.  Your problem then simplifies to this:

$${5 \over 3n^2} \times({ {(\sum_{k=1}^{n}k^3) - n^3}})$$

babyslapmafro · Answer

Ok, thanks, I'll try and take it from here

slaaibak · Answer

Shot.  You're going to have to know the closed form for summing up to n for a cubic series

babyslapmafro · Answer

Ok, I don't know what that is but I'll try to figure it out by looking in the book