221 
finding the Value of an infinite Series, See. 
+ .0 2 2, 334, 101,169, -^-.0 20, 869,976, 759,^- 
*L > 5 ty 10 
+ .oi 9 , 585 > 9 8 4 >° 4 8 >— -.018,450,810,232,^ 
+ •oi7,44 0 5 0 oi,9SS>7^--oi6,534,i84,679,~ 
+ 8cc. or, if we fubftitute x in this laft feries inftead of 
VV v 1 * 1 r • 
-- 5 —-t- + x the ienes 
• ° 2 5 >9 7 9»° 7 5 *5 ° °> - .024,019,1 15, 661, x 
+ .022, 334, 101,169, xx - .020, 869, 976, 759, x z 
+ .019,585,984,048, a: 4 - .0 1 8,45 0,8 1 0,2 3 2,a: 5 
+ .017,440,001,955, a; 6 - .0 1 6, 5 34, 1 84, 679, x 7 
+ &c. Now the value of this laft feries may be difeo- 
vered by the application of the differential feries 
bx D 1 X X T>™X 3 D 1 1 1 Ar 4 DiVy 5 BvX 6 D vl * 7 
bcc, ‘ 
in the manner following : 
> V | 
Here a is = .025,979,075,500; 
b =.024,019,115,661; 
c =.022,334,101,169; 
d = .020,869,976,759; 
e =.019,585,984,048; 
/ =.018,450,810,232; 
g =.017,440,001,955; 
and h =.016,534,184,679.. 
Therefore 
