
Perimeter of Serpinski Triangle 


Stage 
0 
1 
2 
3 
4 
n 
Perimeter of Figure 
3 
9/2 
27/4 
81/8 
243/16 
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Can you see the pattern? This one is a little harder to see than the last. At stage 1 we add 3/2 to the perimeter in stage 0. Then, each stage after that we continue to add, but we add 3/2 of what we added the last time. So we have a sumation of terms. At stage n, we would have 3 plus the sum of (3/2)^{k} as k goes from 1 to n. Then since you are adding with each additional stage, as n approaches infinity, the perimeter also approaches infinity.
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