summation of powers of consecutive integers

• May 6th 2006, 07:59 AM
abiy3000
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?
• May 6th 2006, 08:04 AM
CaptainBlack
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:

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

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

RonL

RonL
• May 6th 2006, 08:24 AM
abiy3000
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.