Question: 3. Given k lines ((k 2 0) on a plane such that no two lines are parallel and no three lines meet at the same

3. Given k lines ((k 2 0) on a plane such that no two lines are parallel and no three lines meet at

3. Given k lines ((k 2 0) on a plane such that no two lines are parallel and no three lines meet at the same point. Let P(k) be the number of regions into which the lines divide the plane (including the infinite ones (see Figure 82.1). Describe geometrically how the recurrence relation P (k) P(k-1) + k can be obtained. Given that P(0) 1, determine P

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