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Math Help - summation of powers of consecutive integers

  1. #1
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    summation of powers of consecutive integers

    Hi. i'm investigating the formulae for the sums of the powers of consecutive integers an dam supposed to comee up with a generalization like
    (1+2+3+...+r)^k=....
    i've done this for k=1,2,3,4...
    but is there a general formula that does NOT involve Bernoulli numbers?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by abiy3000
    Hi. i'm investigating the formulae for the sums of the powers of consecutive integers an dam supposed to comee up with a generalization like
    (1+2+3+...+r)^k=....
    i've done this for k=1,2,3,4...
    but is there a general formula that does NOT involve Bernoulli numbers?
    Surly you mean:

    <br />
1^k+2^k+3^k+\ \dots\ +r^k=\dots<br />

    Why do you wish to avoid the use of Bernoulli numbers?

    RonL

    RonL
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  3. #3
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    oh

    yes, that's what i meant.
    Well, I don mind the Bernoulli numbers...it's just that my teacher seems to think there's an alternative.
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