# How to convert this sum into an equation? [closed]

How to convert this sum into an equation?

$$\sum_{i=1}^{C-1} i(R-i)(C-i)$$

Expanded:

$$\sum_{i=1}^{C-1} (RCi - Ri^2 -Ci^2 + i^3)$$

Which can be represented as:

$$RC\sum_{i=1}^{c-1}i - R\sum_{i=1}^{c-1}i^2-C\sum_{i=1}^{c-1}i^2 + \sum_{i=1}^{c-1}i^3$$

Using the Faulhaber formula and having n = c-1, it can be represented as:

$${1\over 2}RC(n^2+n) -{1\over6}R(2n^3+3n^2+n) - {1\over 6}C(2n^3+3n^2+n)+{1\over4}(n^4+2n^3+n^2)$$

But the results from the sum and the formula from the Faulhaber formula are different. Where is my error?

## closed as off-topic by Leucippus, JonMark Perry, José Carlos Santos, Brian Borchers, user223391 Mar 25 '18 at 0:12

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Leucippus, JonMark Perry, José Carlos Santos, Brian Borchers, Community
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• You mean, simplify this ? – Shailesh Mar 21 '18 at 2:59
• I don't see any error in what you did. Maybe your sum is incorrect? – Ross Millikan Mar 21 '18 at 4:24
• You are correct. There was an error in my sum. Marked your answer as correct since I wasn't sure it could be solved using Faulhaber's formula. – smash87 Mar 21 '18 at 4:57

Expand the product, which will give terms in $i, i^2,$ and $i^3$. Do you know how to sum each of those by Faulhaber's formula?

• I tried using this but I don't get the same result. – smash87 Mar 21 '18 at 3:53
• The same result as what? Yes, that is what you are looking for. If we don't see your work we can't find the problem. – Ross Millikan Mar 21 '18 at 3:55
• I just edited the question to add the procedure – smash87 Mar 21 '18 at 4:11