172k views
5 votes
If n lines are drawn in a plane, how many regions do they separate the plane into? induction

User Shanabus
by
7.7k points

1 Answer

4 votes
Hello,

Let's assume i the number of lines,
u(i) the number of regions:


u_0=1\\\\ u_1=2=1+1=1+u_0\\\\ u_2=4=2+u_1\\\\ u_3=7=3+u_2\\\\ u_4=11=4+u_3\\\\ u_5=16=5+u_4\\\\ ...\\\\ \boxed{u_(n+1)=(n+1)+u_(n)}\\\\ u_(n+1)=(n+1)+n+(n-1)+...+1+u_0\\\\ \boxed{u_(n+1)= ((n+1)*(n+2))/(2)+1 }
User Triet Nguyen
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories