# Math Help - summation of powers of consecutive integers

1. ## 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?

2. 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:

$
1^k+2^k+3^k+\ \dots\ +r^k=\dots
$

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

RonL

RonL

3. ## 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.