Education Technology

Mathematics lessons for IB® Diploma Programme

Analysis and Approaches | Numbers and Algebra

Sum of Infinite Geometric Series

This lesson involves clicking on a slider to see that the area of a square that has been systematically divided into an infinite number of pieces approaches 1.

Planning and Resources


  • Students will understand how a unit square can be divided into an infinite number of pieces.
  • Students will understand a justification for the following theorem: The sum of the infinite geometric series 1/2 + 1/4 + 1/8 + 1/16 + ... = 1.
  • Students will be able to explain why the sum of an infinite geometric series is a finite number if and only if |r| < 1.


  • geometric series
  • infinite series
  • ratio of a geometric series
  • sigma notation