Calculate this awesome limit!

Calculus Level 4

Suppose that circles of equal diameter are packed tightly in nn rows inside an equilateral triangle. If AA is the area of the triangle and BB is the total area occupied by the nn rows of circles, then find the limit of the ratio BA\frac{B}{A} (correct to 3 decimal places) as the value of nn approaches infinity.

The above figure shows the case for n=4n = 4

*Courtesy : Stewart Calculus Early Transcendentals Sixth Edition *

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