The principal goals of this worksheet are To aproximate a Piecewise Continuous Function through Trigonometric Polynomials commonly called Fourier Partial Sums or Finite Fourier Series, to show the convergence of these aproximation via Bessel's Inequality and using Maple spreadsheets and to show Maple’s powerful graphics tools to visualize the application of Weierstrass's Theorem. The attached .zip file contains both the original Maple 8 .mws file and a Maple 10 .mw version of the worksheet.