n lines in a plane

Hello, anujgargcool!

Quote:

Find the maximum number of points of intersection and
number of regions formed by $n$ lines in a plane $(n=0\text{ to }6)$

. . $\begin{array}{c|c|c}<br /> n & \text{Points} & \text{Regions} \\ \hline<br /> 0 & 0 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 4 \\ 3 & 3 & 7 \\ 4 & 6 & 11 \\ 5 & 10 & 16 \\ 6 & 15 & 22 \\ \vdots & \vdots & \vdots \end{array}$

See the pattern?

. . $\begin{array}{ccc}n(\text{Points}) &=& \dfrac{n(n-1)}{2} \\ \\[-3mm] n(\text{Regions}) &=& \frac{1}{2}(n^2+n+2) \end{array}$