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Show that $n$ lines separate the plane into $\frac{(n^2+n+2)}{2}$ regions if no two of these lines are parallel and no three pass through a common point.

I know we start with the base case, where, if we call the above equation P(n), P(0), for 0 lines would be 0. But I really have no idea how to begin the inductive step. How do we know what k+1 we're supposed to arrive at?

Thanks!

  • 0
    looks like $\binom{n-1}{2} + 1$2012-10-09
  • 0
    See also: http://math.stackexchange.com/questions/339750/greatest-number-of-planes-we-can-get-when-dividing-with-lines-and-circles2016-10-03

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