**(Discrete Mathematics Techniques I)**

**Abstract**

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.