A Finite, Infinite Sum
Title: A Finite, Infinite Sum (6th-12th grade)
Presenter: Ruth Vanderpool Ph.D. Lecturer at University of Washington Tacoma
Activity: This activity runs about 40 minutes and builds the geometric sequence
1/2+1/4+1/8+1/16+1/32+… with paper in such a way that students can see that the infinite sum converges to one. Older audiences that are comfortable with lines (9th-12th grade) can verify their conclusions with a historical proof presented in Hairer & Wanner’s Analysis by Its History. Further consideration will be given to additional geometric sequences such as 1/3+1/9+1/27+1/81+… and perhaps students can discover 1/r+1/r^2+1/r^3+1/r^4+…=1/(r-1).