Exercise 15.

Suppose you draw \(n\) lines in the plane so that every pair of lines cross (no lines are parallel) and no three lines cross at the same point. This will create some number of regions in the plane, including some unbounded regions. Call the number of regions \(R_n\text{.}\) Find a recursive formula for the number of regions created by \(n\) lines, and justify why your recursion is correct.