Two lines drawn in a plane separate the plane into three different regions if the lines ar...

Two lines drawn in a plane separate the plane into three different regions if the lines are parallel.

If the lines are intersecting, then they will divide the plane into four regions.

Thus, the greatest number of regions into which two lines can divide a plane is four. Determine the greatest number of regions into which a plane can be divided by 3 lines, 4 lines, 5 lines, and 10 lines. Generalize to n lines.