In fact, when we cut, we will find that after the nth straight line is cut, there will be n more copies.
Namely:
F(n)-F(n- 1)=n
F(n- 1)-F(n-2)=n- 1
...
F(2)-F( 1)=2
Cumulative:
F(n)-F( 1)=2+3+...+n=(n+2)(n- 1)/2=(n? +n-2)/2=n(n+ 1)/2- 1
F( 1)=2。
F(n)=n(n+ 1)/2+ 1