[ 344 ] 



T>ET A -^ B' -a + 6Z+CZ-- + £izi + &c7) Then making z -o, 

 and fubllituting for z, z 



t =bz 



B= I. 2 cz" 



B 



or — = cz'^ 



I. 2 



B — 1 . 2. 3 dz'i 



B 



1.2. 



B 



= a'^5 



B = r. 2. '?• 4 f «'' = ^^* 



"^ ^ I.. .4 



&c. &c. 



&c. 



Whence from the equation A = B' we have by Cor. Prob. 1. 

 K = na bz 



A = 2. «^ cz^ + ff. K — I a b^ z^ 



A = 3. 2 «^ d'srs + s. 2.«« — Id bcz^n.n — \. n — 2 (^'2' 

 &c. &c. 



A 



n «— I 



,A=.a + A + -- +&c. = a + «a ia + - a A'z^ + — 



1. 2 1, 2 * 



" — 2 n.n — i.n — 2 '' — 3 



i 3 



-a i'z'-|-&c. 



«— X n — a 



I f z - + n. n — I a i f a ' 4" ^'^• 



w — I 



-j- n a d z'^ ■\- &c. 



&C. &c. 



The 



