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?


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