Finite Summation of Integer Powers x p , Part 1
Assad Ebrahim · 2010
We solve the finite-summation-of-integer-powers problem Sp(N) = PN k=1 kp using recurrence relations to obtain closed form solutions for any individual p. We motivate the approach and illustrate the method for small p: k, k2, k3, k4, including the use of the computer algebra sys-tem Maxima to assist in the derivation. The general case kp for arbitrary p is treated in Part 2 (Iterative Solution using a p-th order Recurrence) [Ebr10] and Part 3 (Direct Solution using a Matrix Method) [EO10] of this three-part paper.