Rent for a DAY: Illustrate Third of Square or Triangle

What is one third?
What do most kids think of when you ask them about simple fractions such as one half, one third, etc. I have used series models to stimulate discussions about fractions and some of the beautiful ideas behind them. There are numerous nice models or processes. Here are two of them for one third (1/3). The side length is about 50mm; the wall is 1mm thick and 5mm or 10mm high.

Question: What is the sum of all the squares/triangles with bottoms, if we allow the pattern to go on forever and ignore the walls between them?

In general, let R be a real number with R > 1. Then,

\left \sum_{i=1}^{\infty} \frac{1}{R^i} = \frac{1}{R-1}. But, what does it look like at least in some cases?

-------------------------

Ajman FET offers Resources for Self Learners- Unschoolers- Homeschoolers. 
Inspiration, Motivation for Self Learners,Makers, Tinerers & Resources for Discovery (Maker centered) based Learning Right here in Ajman

Terms:

- Refundable Deposit of AED 200 is to be made. We will deduct the Rent and Refund the money to you.  

- Rent will be calculated from 1) Handing over the Model to you or Courier in Person, till the time the model is Delivered back. One day : 24 Hours +/- 4 Hours.

- The Cost here is For Renting the Model for A Day. Collect from and return to Ajman Shop yourself . Collection is Free. We encourage you to get it collected from our Ajman shop

or We ship to you at extra AED 30 Dirhams and you ship it back at Own cost. 

-