Pls solve the Question Fast.....Mixed Approach of 3d and P&C

Hello students

Let number of regions fornlines beR(n)
Clearly,R(1) = 2, R(2) = 4, ...
R(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
=2+2+3+4+....+n
=1+ n(n+1)/2
=(n²+n+2​)/2

I hope this answer will help you