Mathematics Topics: The students will explore the concept of a convergent infinite series using partial sums. This activity connects a number of algebra and geometry topics, as well as to involve students in formal calculations, visualizations, pattern discovery and iterations.

Mathematical Thinking: Students will be asked to investigate numerically and visually the sums of infinite series. Students will further conjecture and prove their ideas behind the sums of specific infinite series.

Technology: This activity uses several Sketchpad commands such as: New Sketch, Midpoint, Segment, Iterate, Polygon Interior and Area.

The following sketches illustrate geometric representations of three different convergent infinite series summing to 1/3, 1, and 1/4 respectively.