ALGEBRA. 41 



193. Prove that every A. p. is a recurring series and th.v 

 rating function is ,,_ / , a being the first term and b 



the common difference. 



194. Find the generating functions of the following series 



(1) 

 (2) 

 (3) 

 (4) 

 (5) 

 (6) 



and employ the last to prove that the integral part of (^3 + 1)*" is 



It- l>y 2" +l , n being any integer. 



195. The generating function of the recurring series whose 

 first four terms are a, b, c, d t is 



ab* -ca' + x (a'd - Zabc + b 9 ) 



19G. If the scale of relation of a recurring series be 



a.- 70.^ + 12^ = 0, 

 and if w a = 2, t/ t = 7, find u m and the sum (f the series 



.?' 



197. Prove that, if 



o,, a u a,. ..a. be an A.P. and 6 6 4 ..., b m a o 



the scries 



are recurring series. 



