(Discrete Mathematics Techniques I)
We motivate an approach that uses recurrence relations to find closed form solutions to the finite-summation-of-integer-powers problem for any individual . The approach is illustrated for small : . Maxima, an open-source (free) software package, is used to demonstrate how a symbolic computation platform can speed up the accurate derivation of messy algebraic expressions.
A recurrence solution to the general case (arbitrary ) is developed in Part 2 along with Maxima source code. A direct (non-iterative) matrix method for solving the general case is given in Part 3 along with Maxima and Octave/Matlab source code.