This is a second version of another sketch I made stacking an image of my head instead of the logo. That can be found here:
[url]http://www.geogebratube.org/material/show/id/3668[/url]
My pre-Calculus students were having trouble visualizing what it meant for a geometric series to converge. They understood the formula aspect and how to calculate the value of a convergent sum, and saw what it meant for numbers adding successively, but I knew there had to be a way to show them.
I had visited Russia with my wife during the winter holidays and saw some amazing arrangements of stacking dolls. I thought at the time about the concept of common ratio, but didn't think about its application to series. Later on, when Dan Meyer posted about a video about stacking dolls (<url>http://blog.mrmeyer.com/?p=10211</url>) I realized this was a perfect way to present and explore convergence.
