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(Sierpinski's Triangle) The fractal called Sierpinski's triangle is the limit of a sequence of figures. Starting with an equilateral triangle with side length 1, the
(Sierpinski's Triangle) The fractal called Sierpinski's triangle is the limit of a sequence of figures. Starting with an equilateral triangle with side length 1, the triangle is split into four smaller equilateral triangles and the middle triangle is removed. Then, for the remaining three equilateral triangles, each are split into four smaller equilateral triangles and the middle triangle is removed. And this process keeps going. Let Tn be the total area of removed triangles after stage n of the process. The area of an equilateral triangle with side length L is A = 3 L2/4 Find T1, and T2, the total removed after stages 1 and 2, respectively. Find a formula for Tn . Find Tn What is the area of the original triangle that remains after n rightarrowinfinity
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