Straight lines dividing a plane into maximum number of regions

To find maximum number of regions in to which ‘n’ straight lines can divide a plane:

“Maximum number of regions can be achieved when the lines are drawn such that no two are parallel and no three are concurrent”
Let us go case by case starting with one straight line.

One straight line can divide a plane into 2.

Two straight lines can divide a plane into 4.

Three straight lines can divide a plane into 7.

observe the sequence: 2, 4, 7,....

If we observe, it is a special sequence which can be written as

1+1, 3+1, 6+1,......
= (1)+1, (1+2)+1, (1+2+3)+1,.....

= ∑1 + 1, ∑2 + 1, ∑3 + 1,......

So, we can generalise like this:

Maximum number of regions that ‘n’ straight lines can divide a plane = ∑n + 1 = n(n+1)/2 + 1