Home

Home | Algebra | Patterns | Recommended Investigations | Half-Sums


half-sums


Consider the infinite sum 96 + 48 + 24 + 12 + . . . , where each term is half the previous term and the pattern continues without end. The sum of the first ten terms is 191.8125. The addition of each new term gets you halfway between the sum of the previous terms and 192. So the sum gets very close to 192. Next, consider the sum 72 + (-36)+ 18 + (-9) + 4.5 + . . ., where each term is(-1/ 2) times the previous term and the pattern continues without end. This infinite sum also gets very close to some integer. Find this integer.


 Extensions

Give an example of a list of numbers with an infinite sum equal to 80.

(Source: Adapted from Mathematics Teaching in the Middle School, Mar-Apr 1997).


 Related External Resources

Pancake Man
Determine how many pancakes a person eats if his / her intake doubles every ten minutes.

The Tortoise and the Hare Race
This investigation examines the process of a race through Zeno's paradox. Investigation questions are provided.

Visualizing an Infinite Series
View the consecutive terms of a geometric series in terms of the areas of segmented trapezoids.

Submit your idea for an investigation to InterMath.