A single line divides a plane into two regions. Two lines (by crossing) can divide a
Chapter 5, Problem 52(choose chapter or problem)
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 \(P_{n}\) 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 \(P_{k}\) in terms of \(P_{k−1}\), for all integers k ≥ 2.
b. Use iteration to guess an explicit formula for \(P_{n}\).
Text Transcription:
P_n
P_k
P_k-1
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