Divergent Series and Convergent Series

A black, green and grey exhibit table with vertical information panel and a series of red and white blocks on the table surface.
A black, green and grey exhibit table with vertical information panel and a series of red and white blocks on the table surface.

Not all series explode to infinity. Some get closer and closer (they converge) to a number.

How it works

Divergent Series: Stack four loose blocks on top of a fixed block, so the top block overhangs to reach a line one block length away.

Convergent Series: This is a thought experiment which challenges you to cover up a square, then a rectangle, by half its area each time. Can the area ever be truly covered?

Things to try or ask around the exhibit

  • Does the top block reach the farthest line on the backboard?
  • If you had to reach a line two block-lengths away, how many blocks would you need to stack above the fixed block?
  • Is there a pattern in how far each block overhangs its block underneath?

Background

To reach the farthest line (which is actually one block length away from the fixed block), you need to stack four blocks so they overhang by: half, then by one quarter, then by one sixth, then by one eighth. By making the blocks overhang one another by these amounts, you’re adding these fractions together. Even though the fractions get smaller and smaller, the total of the series grows to infinity.