Is there an answer to the math problem of cutting watermelon? 1 knife: 2 pieces, 2 pieces, 4 pieces, 3 pieces, 7 pieces, 4 pieces, 1 1 piece .....

Fn=(n？ +5n+6)/6

This problem is actually a problem that n planes can be divided into several parts at most.

The number of parts into which a partition element is divided.

Points are divided into straight lines, straight lines, planes and plane spaces.

0 1 1 1

1 2 2 2

2 3 4 4

3 4 7 8

4 5 1 1 15

5 6 16 26

… … … …

n- 1 P(n- 1)= n L(n- 1)F(n- 1)

n P(n)= n+ 1 L(n)= P(n- 1)+L(n- 1)F(n)= F(n- 1)+L(n- 1)

So l (n) = p (n-1)+l (n-1) = n+n-1+n-2+…+1+p (0) = n (n+/kloc

F(n)=F(n- 1)+ L(n- 1)

=[(n- 1)n/2+ 1]+[(n- 1)(n-2)/2+ 1]+…+[ 1 *( 1+ 1)/2+ 1]+L(0)

= n+ 1+[ 1 * 2+2 * 3+3 * 4+……+(n- 1)n]/2

= n+ 1+(n- 1)n(n+ 1)/6

=(n？ +5n+6)/6