I know this is not a big theoratical question but I need help solving this:


I need to resolve this by getting (if possible) an equation without any sommation. I think what I am trying to find is called a partial summation equation.

Here is what I have done so far:

$$ \sum_{i=1}^{n}{\sum_{j=1}^{m}{(i^2+j^3)}} =\sum_{i=1}^{n}{[\sum_{j=1}^{m}{i^2}+\sum_{j=1}^{m}{j^3}]} =\sum_{i=1}^{n}{[(m*i^2)+\sum_{j=1}^{m}{j^3}]} $$

Now I would like to "get ride" of $\sum_{j=1}^{m}{j^3}$. I have this formula that could be of help:


But I don't know how to apply this formula because $j=1$ not $j=0$ I am not looking for the answer as I would like to solve this by myself I would like for someone to help me with the step of removing $\sum_{j=1}^{m}{j^3}$.

Thank you all!



  • $\begingroup$ Thank you this is all I need! And thank you for not spoiling the answer! $\endgroup$ – Sebastien Jan 13 '16 at 13:39

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