iiO Rev. G. Phillips on the Summation of Series. 



7. To sum the series i^,2\'6\..n^ '^ 2\-i\..n+ \ ^ "^'^''' 



Let r = .-lA + ^=^ + ^— =n + &c. 



Jn 1.2. 3.. .71 2.3...H+T 3.4...7J + 2' 



where /^ may be obtained by the ordinary methods, 

 yj/^i/ -""^3//" " P.2^3\..7J^ + 2^.3^... ;iTT^ 



yn+2 



+ -^ ^^ + &C. 



3^4.^... ?j + 2 



Let /^ / ... n — l^f Jn = u . f L 



JyJy Jy- ""-^ Jy- 



Then as before 



+ 2T3- ''n-,fj,fn-^C. 



yn—\ P ~ 1 /» n— 1 



H ^^ — r, uq I L ->r : I y . r„ 



between the limits of 3/ = and ^ = 1, we have 



P.2^3^..w^ 2^3^..?7+T^ 3^4°%..« + 2 



1 + L-=,+ 1 



l^2^..."^^^^« ' 2^3^...7^^w+^ 3^4^...«+T^^^^2 



+ &c. 



2 Vp.2^...«-2''«-l^.«'^ 2^3-...»^'w.?Mn)J"^ 

 + &c. 



- 1 ( 1 I 1 



■^ 1.2.3..:^^^ P.2.3...W "^ 2^.3.4.. r^TTT 



+ L=:^ +&C.) 



3^4.5...« + 2^ ^ 



"^ 1.2.3...n-l'^ 1.2.3...?z" 2.3.4...n+T* 



+ ^-=^ + &c.] 



3.4.5...n + 2^' ■' 



The 



