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Infinite Geometric Series Using Area of Triangles

Author:Anastasia, Irina Boyadzhiev
Given is an equilateral triangle with Area=1. The vertices of the blue triangle are the midpoints of the sides. 
  • Drag the slider n to construct equilateral triangles inscribed in the white triangle directly above each blue triangle.
  • Click the "+" button to ZoomIn at the vertex of the triangle.
  • Click the "-" to return to the original triangle.
What will be the sum of the area of the blue triangles if we continue to inscribe them to infinity?

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