Infinite sum of areas

An equilateral triangle A1B1C1 is constructed above the height of the equilateral triangle ABC is constructed as. Above the height of the equilateral triangle A1B1C1 is built triangle A2B2C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all triangles if the ABC triangle has a length? And?

Correct answer:

s =  1.7321 a2

Step-by-step explanation:

S = 3/4 a2 a1 = 3/2 a  S1 = 3/4 a12 = 3/4  ( 3/2 a)2 S1 = 3/4 S  S2 = 3/4 S1    q = S2/S1 = S1/S = .. q=43=0.75 q<1  s=1q3/4=10.753/4=3=1.7321 a2



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