From n- 1 to n-k, nk additions (NK) and subtractions (1+2+) are obtained by expansion, expansion and combination. . . k)

Arithmetic progression sum: 1+2+. . . k=( 1+k)k/2

Arithmetic progression sum in the second half: 1+2+. . . (k- 1)=k(k- 1)/2

Together, it is NK-(1+k) k/2-k (k-1)/2.

The latter two items are combined to get the answer.