34rO Rev. G. Phillips o7i the Summation of Series. 



the summation of others, which is performed by the ordinary 

 methods. The principle here employed is of very extensive 

 application, and may be applied to examples whose sums it 

 will be extremely difficult to obtain in any other way. 



The following series are of very considerable generality, 

 and are also remarkable for the neatness of their results. 



1. To sum the series 1 ■ -\ j- &c., &c. 



X'^.l 2"*. 3 3"*.4 



.-./-i/'i-... ^^/'-^ = -^ +J^L + _^+&c. 

 Jy y Jy y Jy i-y j"* 2"* 3'" 



And 



^ yj y y Jy y '" ^ Jy^-y x^^.i 2"". 3 3"*. 4 

 + &c. 



Let now / — f — &c. ... m—\^l = u^_-y 



-^yyjyy Jy ^-y 



■fyfy- -yfy-y - "^^^fy. i-y^fy""^-' 



fy^ «..-2 = «^-2 y-fy^ «^-3 



j y. ^^-3 = "m~3 ^-Jy^-i 

 &C. 



fy^u,= u,.y-f^u. 



