56 



Trans. Acad. Sci. of St. Louis. 



of series may be derived by applying the property named, 

 thus: 



If a, h, c, d, . . . . represent any series of integers, 

 positive or negative, the set of series in which the w'* 

 term of any series is equal to the sum of the first n terms 

 of the preceding series will be : 



a b c 



a a+b a+6+c 



a 2a + h 3a + 26 + c 



a Sa + b Qa + Sb + c 



a 4a + b 10a ^ 46 + c 



d 



a + b + c + d 

 4o + 36 + 2c + d 

 10a + 6b + Sc + d 

 20a + 106 + 4c + d 



Table 31. 



Table 31 may be arranged diagrammatically as in 

 Table 32. 



+ 



a + 



c + 





 

 

 

 





 

 

 

 



1 



1 



1 



1 



1 



6 + 



d + 



Table 32. 



