As shown in figure (1), an equilateral triangle with a side length of 1 is divided into three equal parts, and a small equilateral triangle with a side length of one third of the original side length is grown outwards to obtain figure (2), which is called "primary growth". Similar to "growing" on the obtained polygon, * * * grows n times. What is the perimeter of the polygon?

The original picture is on the left, with a circumference of 3;

1) After the 1 th increase, as shown in Figure 2, each side actually increased 1/3, so the perimeter also increased1/3; That is, the perimeter after the 1 th growth is the original1+1/3 = 4/3;

2) After the second growth, as shown in Figure 3, each side actually increased by1/3 compared with each side in Figure 2;

So the perimeter after the second growth is1+1/3 = 4/3 after the first growth;

……

By analogy, after growing n times, the circumference is (4/3) n of the original figure;

∴ The circumference after N times increase is: 3 * (4/3) n = 4 n/[3 (n- 1)].