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# Begin with an equilateral triangle whose area is 1 square unit (Iteration 1). Divide the triangle into 4 equal areas (all equilateral triangles) and

Can someone help me figure out this calculus problem I don't know where to start.

Begin with an equilateral triangle whose area is 1 square unit (Iteration 1). Divide the triangle into 4 equal areas (all equilateral triangles) and color in the center section {Itera-
tion 2). Do the same with the remaining 3 areas {Iteration 3). How much of the triangle is now colored in? Repeat with the remaining areas [Iteration 4]. How much of the area
is now colored in? Continue dividing the remaining areas. How much is colored at each stage“? If this process is continued forever, how much of the area will be colored in? Justify your an-
swer by writing an inﬁnite series that represents the colored area and then evaluating the series.

(1/4) (1/4) + (1/4)*(3/4) (1/4) +... View the full answer

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