Summation of certain Types of Series. 81 



(ii.) Let u lt _i designate the nth term of the given series, 

 then 



it* 



- 1 



and 



n(4+«) n(ii+«) 

 "-' n(4+«) n(ii+«) " + l 





= r S (n + 4)?/„, 



and since (n + 10)u n '\ n _ Q = 10, w being 1 

 therefore 



and 



or 



Hence 



2 (n + 10K = r 2 (w + 4> n + 10, 

 r(l-r)^+(10—4r)S=10, 



<7S,10-4r Q 10 



dV r(l— r) Wl — r) 



fl0-4r . r- /'* 1 ("10— 4r 



S = e -i*&5* [0 + 10 J j;— ,.fe' 



aV 



r ?' 9 



J^rr^/^i letl-r = «, 

 -g)(l-,)e l0S (l-,)-(i)(l-^ + ®^ 



To obtain 

 then 



Therefore 



PAt7. A/a?. S. G. Vol. 31. No. 181. Jan. 1916. 



G 



