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General formula for summing powers of r? watch

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    Is there a general formula for summing various powers of r. I've tried looking around on the internet but can't seem to find anything (well, either that or I'm searching for the wrong things )

    What I mean is that I know there is a formula for \displaystyle\sum_{r=1}^{r=n} r,  \displaystyle\sum_{r=1}^{r=n} r^2 and \displaystyle\sum_{r=1}^{r=n} r^3 but is there any way to incorporate all of those into one big general summation?

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    (Original post by silentshadows)
    Is there a general formula for summing various powers of r. I've tried looking around on the internet but can't seem to find anything (well, either that or I'm searching for the wrong things )

    What I mean is that I know there is a formula for \displaystyle\sum_{r=1}^{r=n} r,  \displaystyle\sum_{r=1}^{r=n} r^2 and \displaystyle\sum_{r=1}^{r=n} r^3 but is there any way to incorporate all of those into one big general summation?

    Thanks for helping
    No, I'm afraid not - the relevant section of Wikipedia is https://en.wikipedia.org/wiki/Harmon...Generalization and https://en.wikipedia.org/wiki/Faulhaber%27s_formula but that requires knowledge of the Bernoulli numbers and the evaluation of a related sum.
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    http://nrich.maths.org/267

    This is an investigation I did a few months ago on what you are concerned with, spend some time doing the activity and you'll understand how to derive it!


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    (Original post by Smaug123)
    No, I'm afraid not - the relevant section of Wikipedia is https://en.wikipedia.org/wiki/Harmon...Generalization and https://en.wikipedia.org/wiki/Faulhaber%27s_formula but that requires knowledge of the Bernoulli numbers and the evaluation of a related sum.
    That seems a bit too complicated for me ATM, maybe I'll be able to get back to it sometime

    [QUOTE=Omghacklol;48374242]http://nrich.maths.org/267

    This is an investigation I did a few months ago on what you are concerned with, spend some time doing the activity and you'll understand how to derive it!

    I was searching for something like this, it seems like a generalized version of the method of differences for powers of r which is what I was trying (and failing) to come up with

    Posted from TSR Mobile
 
 
 
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