igoS.j 



IN INFINITE SERIES. 115 



and denoting the continued product 



(i -{- sk~n) (i -\-sk — 2)i) (i + sk — 311) ■•■[i -\-sk — (s — i)n] 

 by 



^ ^^ 1. 1 -\- s/^ — sn A 



With these conventions series (13) becomes 



If series (15) is convergent, it will furnish a root of the three- 

 "term equation 



for each one of the n values of Vq. 



10. To test series (15) for convergency write the first n terms in 

 regular order in a row, underneath this row the succeeding n terms 

 and so on indefinitely. The terms of series (15) will now be arranged 

 in n columns as follows : 



