Polynomial Division can be used to find Taylor polynomials of rational functions easily and quickly. The polynomial division that does this trick is inverted in the sense that, instead of canceling out the leading terms at each step, one cancels out the trailing terms. Otherwise everything goes just like in the ordinary long division of polynomials.

This video explains why the geometric series 1/2 + 1/4 + 1/8 + ... converges using an elementary argument. The video is meant to be preparatory materials for students to view before the discussion of geometric series takes place in a class room. The video finishes with an intriguing example.