8*2 Methods for the Summation of certain Types of Series. 

 Multiplying by r 10 and letting r = 0, we have 



<-i»[HDH1)~«)+G)HS)M?)l-8)H>° 



oi-C = 518. 

 Therefore 



-84(l-r)Mog(l-r)-126(l-r) 5 + 63(l-r) 4 

 -28(l-r) 3 + 9(l-7f-|(l-^) + g] ? 



840 T /i An /in n 2 ?)1 3 , 57 4 S? * 



= 7To-L-( 1 - r ) 6 log(l-r)-r- r2 r 2 -yr 3 + ir r 4 - 



49 fi 1 7 1 8 1,1 

 ^20 7 56 252 J 

 IV. To find 



10 r 



a a(a+l) a(a + l)(a + 2) 



n (a + *) 



S = - + v 7f -f . r /> ' r / r 2 + = 2 - 



6 6(6+1)' 6(6 + l)(6 + 2) 



K=0 



wherein a and b are positive integers and a < b. 

 IL(a + /c) 



K = 



_ (b-l)l (a + n) \ _ (b-1) I 1 



Now 



II (b + tc) v ' v y v y II(n + a4-/c) 



K-0 K = l 



II (w + a + K) 



therefore 

 II (a -f- /c 



:=0 



71 



,i x//'-lV?/ n ,//>-« — 1\ 1 

 = (*-a)( a „l)2(-l) K -\ ,_! ) ? , T , + V 



and 



S=(*-a)( a _ 1 ) K 2(-l>- 1 ( ,_, )^ ^^' 

 = (6-a)( fl _ 1 j 2 ,-1)+^ ..J j-^jE-p^-. 



