Rev. G. Phillips ow the Summation of Series. 343 



- (^ + i + 4^ + «'H 



2* 

 &c. 



\ 2" 3" 4 ' 



1 1 1 Q 



3. To sum the series y^^ + g^^gS + g^T^ + ^<^- 



If in the first ariidej u^_^ = v 



. ^ = _i^ + _i!- + -fV + &c. 



• • ^ i»i_ 2 ^ 2'". 3 3"'. 4 



/* i_ „ _ / ■ _^ + .^^ + &C 

 Jy. y 1"'.2^ "^ 2'«.3'' 3"'. 4^ ^ 



r ^ r ^ ., - y 4. _-.z_- 4. —-^ + &c 



And 



,?/ ^ y 





3*". 4" 



Now we have shown that 



-Jy.Jy i-y 



■'• fy- 7 ' =^. "-^ "X- "-^ "^X- ""'-^ " ^'' 



^ Jy. ~Jy. y Jy.Jy. \-y 

 = u ,.ij — 2u „,y + Su -.w — &c. 



m— I ^ m — l'^ m — 1 -^ 



+ 7n — 1 u,.y + m/ -I / - — - 

 1 ^- Jy. y Jy.Jy. \-y 



fy. jfy. \ ' ^fy:'-^ ' ^fy- "-- ^^y- "'-^ " 

 ''''^'''^fy.''^^''fy.jfy.\fy-fy-T^y 



■y 



— u 



