but remains less than the area of a circle...
area pologon <A given
So how can area ever be this?
area pologon=A+A(1/3+..._ ?
The first term of a an infinite sequence is an equilateral triangle inscribed in a circle. The triangle has side n. Each new polygon in the sequence is formed by replacing the middle third of each side by two segments that have the same length as each third. As n, increases the area of polygon P increases but remains less than the area of the circle. The area of polygon 1 is A. Explain why the limit of the area of polygon p = A + A (1/3 + 4/27 + 16/243 + ...) Let Sp be the area of polygon p. Find the limit of Sp.
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