-4° 6 Mr. vince’s new Method of 
54 12 i 
* - 4-7 • »o. 13.3.5*4.7- 13 - 3 - 4 + 7 • 10 . 13 .3 . 3 ~ 
~~ ' ' ' • 
• UjOUO 
By this proportion we may alfo inveftigate the fum of the 
feries when there are any number of deficient terms in the 
denominators, and where the laft differences of the numerators 
become equal to nothing ; for if the factors in the denomina- 
tors be completed, and the numerators be multiplied by the 
fame quantities, their differences will flill become equal tQ 
nothing. 
case 1. 'To fnd the fum of the infinite feries 
1 • 3 • 4 • 0 
+ 
+ 
+ 
TO 
■f 
*5 
4~ See. 
2 • 4 * 5*7 3 - 5 - 0 - 6 4 «*>« 7'9 5.7.8.. 10 
Tins fe lie.?, bv completing the fadfors 111 the denominators 
and multiplying the numerators by the lame quantities, becomes 
10 ca 168 
+ &C. ill which 
+ 
+ 
3 . 4 . 5 . 6 . 7 . 8 
1 . 2 . 3 .4 .5 . b 2. 3. 4. 5. 6. 7 
cafe n~i y m ~ 1 , r~ 3, and as the 5th differences are 
.*. £ 4 -^ 4 - 2 £* 4 - 6^-f 24^= 10, a 4- zb 4- 6 c + 2s{d+ 1 zoe=: 54, 
a + 3 ^ + 1 2C + 60^4-360^168, ^ 4 - 4^4- 20C4-1 20^48401?=: 400, 
a + 5^T3 0<r T-2io^-f-i68od’=: 810, from whence a~ o, ^ = 0, 
czz *"* o, ezz confequently the fum of the given feries is 
4 - 
3 • 4 • 5 • 3 5 • 2 
dl 
180 * 
case 2. To find the fum tf the infinite feries 
$ L, 11 r 19 
3 • 5 * 9 • 11 ~5 • 7 . 11 . ,3*7 . 9 . 13. 1 s +6CC * 
By proceeding as before this feries becomes 
1 - 3 - 7<9 
1 • 3 • 5 • 7 • 9* 
3 $ 
