Without giving it much thought, it seems like the limit should just be the area of the triangle, which is
EDIT: Nevermind. I misread your question. A formula that might help you is that Try to find a formula for For example,
Let T be the equilaterall triangle with sides = 1 length.
Let be the # of circles that can be packed tightly in n rows inside the triangle.
Let be the combined area of the circles. Find the limit of as n -> infinity.
I believe I have to find a series for the number of circles in the triangles, right? So I need to find something to represent 1, 3, 6, 10, 15 ... ?