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Suppose we we have n straight lines on the plane such that no two of them are parallel and no three of them go through the same point. Prove that the number of different regions that are created by these lines (regions that are bounded between line segments and/or those that are unbounded) is exactly $\frac{n(n + 1)}{2} + 1$ for all n ≥ 1.


marked as duplicate by Brian M. Scott discrete-mathematics Mar 12 '15 at 4:27

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  • $\begingroup$ You may also find this question and this one (and their answers) useful. $\endgroup$ – Brian M. Scott Mar 12 '15 at 4:28
  • $\begingroup$ in base case if n holds for 1 and 2, then we can conclude that p(n) holds, $\endgroup$ – Tiina Mar 12 '15 at 4:28