My task is to develop a formula for the perimeter of the nth stage of the sierpinski triangle.

develop a formula for the perimeter of the nth
stage of the sierpinski triangle.
Figure: Deterministic construction of S
Clearly
Now let the side of triangle be a in stage 0
Now in next stage stage 1 :
Length of side of triangle is : a/2 (can be observed clearly)
Now in next stage , stage 3:
Length of side of triangle is : ...