51. Connecting Geometry and Sequences In the following sequence of diagrams, regular polygons are inscribed in unit circles with at least one side of each polygon perpendicular to the positive x-axis.
(a)
(b)
(c)
(d)
(a) Prove that the perimeter of each polygon in the sequence is given by an=2nsin(π/n), where n is the number of sides in the polygon.
(b) Investigate the value of an for n=10,100,1000, and 10,000 . What conclusion can you draw?