Sums of Powers of Integers and Bernoulli Numbers Clarified
Theory and Applications of Physical Science Vol. 2,
Page 28-40
Abstract
We exposes a very simple method for calculating at the same time the sums of powers of the first integers and the Bernoulli numbers . This is possible thank to integrations of the equation which lead to a formula saying that the vector is the transform of the vector by a matrix built from the Pascal triangle and obtainable by a simple algorithm. Very useful relations between the sums , the Bernoulli numbers are deduced, leading straightforwardly to known and new properties of them. The proof of the Faulhaber formulae on powers sums are outlined briefly at the end.
We exposes a very simple method for calculating at the same time the sums of powers of the first integers and the Bernoulli numbers . This is possible thank to integrations of the equation which lead to a formula saying that the vector is the transform of the vector by a matrix built from the Pascal triangle and obtainable by a simple algorithm. Very useful relations between the sums , the Bernoulli numbers are deduced, leading straightforwardly to known and new properties of them. The proof of the Faulhaber formulae on powers sums are outlined briefly at the end.
Keywords:
- Bernoulli numbers
- arithmetic operations
- integers
- Pascal matrix
How to Cite
- Abstract View: 0 times