APICS Mathematics Contest 1984


  1. Does the series converge or diverge? If it converges, find the sum.

  2. Determine all fourth degree polynomials such that there is another polynomial with

  3. Solve for given by

  4. Let T be the matrix and Show that and are equal for each .

  5. Is it possible to find two integers x and y such that the sum of their cubes is 6? Why not? What if x and y are allowed to be rational?

  6. Let f be a twice differentiable function on such that and . If and for all , prove that for all .