Kenneth Rosen Edition 7 Exercise 8.1 Question 22 (Page No. 511)

Question

• A. a) Find the recurrence relation satisfied by $R_{n},$ where $R_{n}$ is the number of regions into which the surface of a sphere is divided by $n$ great circles (which are the intersections of the sphere and planes passing through the center of the sphere), if no three of the great circles go through the same point.
• B. b) Find $R_{n}$ using iteration.