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We provide a simple recursive method for generating the finite sum of whole number powers of integers. Given that we know only the formula for the sum with power p – 1, this method generates the formula for the sum with power p by a simple polynomial integration and a solution to a linear equation in one variable. This method makes no use of Bernoulli's equation or Bernoulli numbers in either its implementation or justification.
R. Brent Dozier (Wed,) studied this question.