Sums of Powers of Integers and Bernoulli Numbers Clarified

We exposes a very simple method for calculating at the same time the sums of powers of the first integers the Bernoulli numbers Bm 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 the Bernoulli numbers m B 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.