Engler — Figurate Numbers. 



41 



Continuing this process precisely as before for the series 

 1, 4, 10, . . . 



Table 4. 

 we obtain as the formula 



njn+l) {n+2)(n+3) {n+4 ) 

 ^ 1-2-3-4-5 



for the sum of the series 1, 5, 15, 35, 70, 126, 210 . . 



From 



(5) 



Table 5. 

 we obtain as formula 



n{n+l) {n+2) (^+3)(^4-4) (n+5) 

 ^ 1-2-3-4-5-6 



for the sum of the series 1, 6, 21, 56, 126, 252 



(6) 



