[ 417 ] 



Then fince I^— = i-^- +-3 + -^ + ^ + 



3cjf' — iS^y 15^5 25/'' 125 jK' 



27 81 , « I, ' t; J^ + 1 10 



— ' + — + &c. we have ■> -^ J — — 



625^" 3i25jy'3 I5_y5 30/5 — i8j 



~ — — - — ^ — — '- — — — &c. which beins 



25^ 125J' 625^)'" Sizsj'^ ^ 



fubfiituted for the fecond and third terms of the feries, we get 



the feries in this form, 2p x — + j 3_- + 



y s'^y' — ^^y ^7sy' 



4+ 328 2072 ,5 a • .u . 



+-r^ 1 ~ — ■ + &c. Again; the terms 



U25_)'' 6»75_)'" 406257'^ 



' and — -— — , (which are of the fame dimenfions with the 



175JK' ii25_y' 



fourth and fifth terms of the firft feries) being reduced to a com- 



mon denominator, their value is — — 1 -^ 1 : which, by a 



procefs fimilar to that already ufed, may be fhewn to be equiva- 

 lent to, 36_ 3_3S8_ _ _26o826_ _ ^^_ 



^sisy^ " ^^9sy' 50625/" 2278125 j"3 



the terms after the firft, decreafing in the ratio of 180 j» : 308, 

 or of 45 J* : 77- 



Then, by fubftitution, the feries comes out in this form : 

 , I , ro , 36 42S 



y 30^5 — iSjf 1575/' — 2695 _y^ 2275 j" 



75236 _ 



ii«4625jF'3 ^'^' 



Vol. VI. 3 G " The 



