1. I have been interested in this paticular problem:

Either there may be a general formula, or there's a systematic method.

I decided to begin by looking at smaller values of m, and hopefully I can find a pattern in the formula.

And so on...

I've found two systematic ways to calculate formulas for higher values of m. The first uses simple algebra, the second involves derivatives.

I'll be happy to share them later, but first I want to see if anyone got their own method that they would like to share. Please post below.

2.

3. Originally Posted by Wise Man
I have been interested in this paticular problem:

Either there may be a general formula, or there's a systematic method.

I decided to begin by looking at smaller values of m, and hopefully I can find a pattern in the formula.

And so on...

I've found two systematic ways to calculate formulas for higher values of m. The first uses simple algebra, the second involves derivatives.

I'll be happy to share them later, but first I want to see if anyone got their own method that they would like to share. Please post below.
If you don't need an exact equation then

for x= 1 to n, ∑ xm ≈ ∫ xm = nm+1/(m+1).

The approximation gets better with large n, as your three examples will show.

4. http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

Above has explicit formulas up to 7th power.

5. Originally Posted by mathman
http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

Above has explicit formulas up to 7th power.
A great source!

6. IMO,you can actually see it as a sequence an A.P as it appears to increase with a particular vale of 1^m.

when i did that you will have n(2^m+1^m(n)-1^m)/2 (sum of an A.P).

7. Originally Posted by mathman
http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

Above has explicit formulas up to 7th power.
I am very disappointed to see, that your link has eff all to do with maths.

8. Originally Posted by Dave Wilson
Originally Posted by mathman
http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

Above has explicit formulas up to 7th power.
I am very disappointed to see, that your link has eff all to do with maths.

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