We present different methods to generalize sums of powers of positive integers in terms of recurrence relations using the Taylor series, and in closed form using a finite difference method and an integral method. The result gained through the integral method is similar to Bernoulli's sum formula, but it is expressed in terms of a certain recursive sequence $H_i$.
"Sums of Powers of Integers." Missouri J. Math. Sci. 31 (1) 66 - 78, May 2019. https://doi.org/10.35834/mjms/1559181627