end Infinite Series. 439 
1 21. Hence alfo we may find the fum of any gene- 
ral feries of either of thefe forms, namely, 
_ 2 s 
3. S 
3.6 3 . 6 . 9 . 1 
1 - or 
2 3..0.9.12.15. 18 
i_ i 2 • al + ± 2 - ;- 8 - 11 • h • 17 g* 
3 3.6.9 3.6.9.12.15 3.6-9. 12.15 
~f ~~ — — - 1 "* I - 4 ’ z R 7jr ~ See. by com- 
. 6- 9 . 12 . 15 . i-S . 21 y 
paring them with the roots of given cubic equations ; 
whatever be the value of g , not greater than 1. 
122. For, by Art.. 68, + c + fib-c - 2 fib x 
8cc. is = the greateft root of the 
1 - 
2-. 5 . Sc 4 
3.6 b z 3 . 6 . 9 . 12 £ + 
cubic equation # 3 — 3^ b 2 -? . x — 2 b. Now make 
2 fib — 1 , and - = g 2 ; fo lhall the above become 
ifi 1 +g + 1 —g — 1 — 1 — ‘ g,r Sec. = the great- 
3.6 
2 • i • v 
3.6.9.12 
- 
eft root of the equation x* - fv 1 -g 1 . x. = \. .And 
2 
when g 2 or - is negative, thefe become 
~fi i+gfi -1 + t-fi 1 -gfi - 1 = 1 + 
ill _ 2 • s • V 
3.6 3.6.9.12 
+ . 8 cc. 
: the greateft root of the equation x 3 - |vi +g 2 . x = ±.: 
So that in general the infinite feries 
I T T 2 d • » • » • HZ &c< is , 
3.6 3.6.9.12^3.6.9.12.15 . i 3 
- ifij~ 7 fi~fi~i + Ls/\ -gV ± 1 = the greateft root of the 
equation v 3 - ly'I . * =■£. Where the upper and. 
under figns refipeitively correfpond to each other.. 
123-. Again, 
