Question 15 and 4. Please solve all problems with detailed steps

15. The semiperimeters of regular polygons with k sides that inscribe and circumscribe the unit circle were used by Archimedes before 200 B.C.E. to approximate 11', the circumference of a semicircle. Geometry can be used to show that the sequence of inscribed and circumscribed semiperimeters {pk} and {Pk}, respectively, satisfy pk = ksin (E) and Pk =ktan (1%), with pk _ 4, the sequences satisfy the recurrence relations n . Approximate It: to within 104 by computing pk and Pk until Pk pk