Monday, 2 January 2017

solving for the inductive step in a proof by induction

Here is the problem




I have no trouble solving for the base case. I need help solving the inductive step. I know that the nth line creates n new regions. But I don't know if that's based on intuition or if I have to prove that. Do I have to prove that the nth line creates n new regions? If so, how can it be done?

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