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



0»! », I 1 I 



Hence it appears that if we can sum the series when each 

 terra has n—)} figures ; we can when it has n figures, but we 

 have summed it when 7i = 2 (Art. 1.) .-. we can when « = 3, 

 and .♦. when w = 4, and generally. 



6. To sum the series r— r-r 5 + -^3 



1.2.3...«2 ^ 2.3.4...^+?^ 



^ +&C. 



3.4 ...«T2l 



2.3...«"4-l^ 



Jijjy. Jy.l^y 1.2.3...«^ 2.3...77TT 



And r^r r ....-^r ^^ r 



-^yy^y-Jy jy.i-y^ 1.2.3... n^ 



-y 



+ ^ f , + &c. 



If r r ..,w=^ r J- ^ ,, 



JyJy Jy. \-y n-x 



We have u . — y .u „— -^- . u a ^ u 



n-\ -J n-2 2 n-3 ^ 2 . 3 «-4 



- &c. 

 2.3...71 — 1 2.3 ... n—ijy. \—y 



fy- 7X'*«-> =^."«-2"iX^""-3 ^ 2-r^.^'"«-4 



+ &c. 



1 >^ M- 2 2 y^ 71—1 



+ ==< / y Wn + =S / ^ 



2.3...71-1 ^.y- 2.3...«^^«>'3/. 1—3^ 



XtX. ^'- ""-3 = 273 "n-3 - f -"-2 + T"«-» 



