3. [10 pts] If n lines (infinite in both directions) are drawn in a plane such that no two lines are parallel and at most two lines intersect at any single point, then those lines partition the plane into a specific number of regions. For example, one line always partitions the plane into 2 regions and two lines always partition the plane into 4 regions. Determine a general formula for the number of regions resulting from n such lines, and prove by induction that your answer is correct. n(n+1