The accompanying figure shows the first three equilateral tri- angles in an infinite sequence of successively smaller equilat- eral triangles formed by connecting the midpoints of the sides of the preceding larger triangle. The largest triangle has sides of length 4. (a) Write the infinite series that represent the total perimeter of all the triangles. (b) Find the total perimeter of all the triangles using the infinite series in part (a).
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The largest triangle has sides of length 4. The next smaller triangle has sides of length 2, which is half the length of the largest triangle. The next smaller triangle after that has sides of length 1, which is half the length of the previous triangle. So, the Show more…
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