0
$\begingroup$

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

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

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:

$$\sum_{i=0}^{n}{i^3}=(n(n+1)/2)^2$$

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!

$\endgroup$
2
$\begingroup$

$$0^3=0\implies\sum_{j=0}^mj^3=\sum_{j=1}^mj^3$$

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.