# Too many circles in a triangle

Calculus Level pending

Suppose that circles of equal diameter are packed tightly in $$n$$ rows inside an equlateral triangle such that there are n circles in $$n$$th row. If $$A$$ is the area of the triangle and $$A_n$$ is the total area occupied by the circles in $$n$$ rows, find $$\displaystyle\lim_{n\to\infty}{A_n}/{A}$$ (the diagram shows an example of $$n=4$$ rows).

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