Confirming a Summation Identity


by eddybob123
Tags: bernoulli number, binomial, identity, power series, summation
eddybob123
eddybob123 is offline
#1
May9-13, 06:24 PM
P: 115
Hi all, I found this "identity" online on Wikipedia, and realized that it would actually come in pretty useful for me, if only I could prove that it is true. Can you guys help me on that?:
$$\sum_{k=1}^nk^m=\frac{1}{m+1}\sum_{k=0}^{m}\binom{m+1}{k}B_k\;n^{m-k+1}$$
where ##B_k## denotes the kth Bernoulli number.
Phys.Org News Partner Mathematics news on Phys.org
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
CompuChip
CompuChip is offline
#2
May11-13, 06:16 AM
Sci Advisor
HW Helper
P: 4,301
Looks like the proof is also on Wikipedia :)
eddybob123
eddybob123 is offline
#3
May11-13, 02:18 PM
P: 115
So the formula in my first post is correct?


Register to reply

Related Discussions
Vector field identity derivation using Einstein summation and kronecker delta. Calculus & Beyond Homework 2
Summation Identity for i^p power question, really simple Calculus & Beyond Homework 2
The Summation Identity (Combinatorics) Calculus & Beyond Homework 0
Confirming and asking questions! Calculus & Beyond Homework 2
Poisson summation and Parsevals identity Calculus 1