
Area of Serpinski Triangle 


Stage 
0 
1 
2 
3 
4 
n 
Area Shaded 
1 
3/4 
9/16 
27/64 
81/128 
? 
Did you find the pattern to be that we multiply by 3/4 at each stage? So, the last entry is (3/4)^{n}. Since 3/4 < 1, we multiply and get a smaller area each time. As the stages converge to infinity, the total area of the triangle goes to zero. Amazing!
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