Question

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

Answer 1

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

Answer 2

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:

\[{5 \over 3n^2} \times({ {(\sum_{k=1}^{n}k^3) - n^3}})\]

Answer 3

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

Answer 4

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

Answer 5

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