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Exploring convergence

Created by yish   -   Topic Group: Sequences   -   Created: 22-03-05   -   Modified: 23-06-05




We are exploring sequences that get smaller but do not go below zero.

Such as:

  • 1, 1/2, 1/3, 1/4, 1/5 ...
  • 1, 1/2, 1/4, 1/8/ 1/16...

The questions we are looking at are:
  • What is the shape of these sequences, and what does it tell us about them?
  • What happens when you sum up the terms of these sequences?

For each sequence, our tasks are:
  1. Model the sequence in ToonTalk.
  2. Predict the shape of its graph.
  3. Use the Excel tool to plot the graph.
  4. Use the add up robot to generate the running totals of the sequence.
  5. Predict the shape of the graph of running totals.
  6. Use the Excel tool to plot the graph.
  7. Publish a webreport with your findings.
If you're modelling the Reciprocals sequence, you may find this worksheet helpfull.