Snowflakes

To construct a snowflake curve , start with an equilateral triangle with side length 1.

Step 1 in the construction is to divide each side into three equal parts, construct an equilateral triangle on the middle part, and then delete the middle part.

Step 2 is to repeat step 1 for each side of the resulting polygon. This process is repeated at each succeeding step. The snowflake curve is the curve that results from repeating this process indefinitely.

Sum an infinite series to find the area enclosed by the snowflake curve. If the area is $\frac{A\sqrt{B}}{C}$ , then what is $A+B+C=?$