Total number of regions in which ' n ' coplanar lines can divide the plane, it is known that no two lines are parallel and no three of them are concurrent, is equal to

Step-by-step solution

Let number of regions for n lines be R(n) . Clearly, R(1)=2, R(2)=4, (n)=R(n-1)+n i.e. R(n)-R(n-1)=n Putting n=2,3, , n and then adding, we get R(n)-R(1)=2+3+ +n aligned & =2+2+3+4+ +n=1+ n(n+1) 2 & = n^2+n+2 2 aligned