000RM.dvi

722 Figurate numbers

27.4 The polygonal numbersPn,k...............

More generally, for a fixedk, thek-gonal numbers are the sums of the

arithmetic progression

1+(k−1) + (2k−3) +···.

Thenthk-gonal number isPk,n=^12 n((k−2)n−(k−4)).