Fractal Squares
Algebra
Level
2
The image above shows a construction of fractal by joining smaller and smaller squares to each side of one single square.
- We start with a square of side length 3.
- In the second figure, the 4 new squares are formed with a side length of \(\dfrac{1}{3}\) of its previous square.
- Then from the third figure and so on, the new squares can only be formed on the 3 sides of the previous squares with side length \(\dfrac{1}{3}\) of its previous square.
As this recursion continues indefinitely, what does the total area of the figure tend to?
by
Worranat Pakornrat