(360 



Dr. I. J. Schwatt on the 



Adding 



(n+6K]^ o = jg 



to both sides 



of the last equation. 



we have 



00 oo J. 



2 (n + 6)u n = r%(n+ l)u n + — 



«=0 ?*=0 " ! 



But 



00 °° ^S 

 X «„ = S and 2 ?im„ = y — j- ? 



or 

 Hence 



dS CQ 2 ^S a 1 



r 3r +6Sa= ^*: +rS+ sT 



-(!-*■)? +(6-«-)S- iji. .... (2) 



e 



s = - 



dr ' v y 5!' 



5! J'Lr(l-r) +C J 



=r,^[JaV +0 ]' • • » 



Now 



4 ^» 5 ^t5 ^,4 ^,3 ^,2 ^, 



J (i^)6^= 5(l-r) 5 ~4(1-^) 4 + 3(1 -ir) 3 " 2(l-r) 2 + 1^ +1 ° g (1 ~ r) 



5 



*(l-r)' 



= s(-ir 1 - 7 ^ 1 - TK +iog(i~r) (4) 



Therefore 



■^-^(-)^[('-JM('-!)' | 



1 (1-r) 5 , M N , 1 H37 77 47 9 



1 /1 ^3 -J 5 5- 



= i^^ log (1 .-r)+ =±- 2 S(-l)*^-V- (6) 



The same result might also be obtained by the following 

 method. 



