Engler — Figurate Numbers. 



51 



sum of the first n terms of the preceding series. In this 

 case the expressions for the sums become : 

 For (e), by (1) and (2) 



^ (n — 1)^ , 



1-2 



For (f), by (2) and (3) 



^ n (n+1) jn—l) n (t^+l) ^ 



1-2 

 For (g), by (3) and (4) 



lr2:3 



^ n(n+l)(n-{-2) (n—l)n{n+l){n-\-2) 

 1-2-3 l-2:3t4 



For (h), by (4) and (5) 



^_ n{n+l)(n+2)(n+3) _j_ 



1-2-3-4 



(n—l)n (t^+l) {n+2){n-\-S) 

 l-2r3:4-5 



d 



For d = 3, these series become 



1 2 5 8 TI 

 1 T 6 14 25" 

 1 6 20 45 

 1 1 5 25 70 



Table 22. 



For 6Z=2, 



Tabic 23. 

 which is identical with Table 14. 



(12) 



(13; 



(14) 



(15) 



