  We realize that geometric polynomials and p-Bernoulli polynomials and numbers
are closely related with an integral representation. Therefore, using geometric
polynomials, we extend some properties of Bernoulli polynomials and numbers
such as recurrence relations, telescopic formula and Raabe's formula to
p-Bernoulli polynomials and numbers. In particular cases of these results, we
establish some new results for Bernoulli polynomials and numbers. Moreover, we
evaluate a Faulhaber-type summation in terms of p-Bernoulli polynomials.
