( 1^3+5× 1+6)/6=2

So it's confirmed,

(2) Assuming that n=k, the conclusion holds.

Immediate segmentation

(k^3+5k+6)/6

A region,

After adding faces,

This face will have k intersections with the previous k faces,

These k intersection lines are all on a new plane, which is divided into

2+2+3+……+k

= 1+k(k+ 1)/2

Part,

Accordingly, the number of spatial regions increases.

1+k(k+ 1)/2 pieces

(k^3+5k+6)/6+[ 1+k(k+ 1)/2)

=[(k+ 1)^3+5(k+ 1)+6]/6

Therefore, when n=k+ 1, the conclusion also holds.