A single line divides a plane into two regions. Two lines
Chapter 5, Problem 52E(choose chapter or problem)
Problem 52E
A single line divides a plane into two regions. Two lines (by crossing) can divide a plane into four regions; three lines can divide it into seven regions (see the figure). Let Pn be the maximum number of regions into which n lines divide a plane, where n is a positive integer.
a. Derive a recurrence relation for Pk in terms of Pk–1, for all integers k ≥ 2.
b. Use iteration to guess an explicit formula for Pn.
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