2io 
Mr. maseres’s Method of 
,1 ,7 ,9 f .I 
Therefore the twelve terms t- — +-jp-y-5+— .-77^5 
<I3 _ ,IS , *1 *1 1 C fll_are 
+ l 37-* 1 I’jr ' 6 I9r‘ s 2ir 10 23*-“ 
' rx 1. 000, 000, 000, 000, -rx. 333, 333, 333, 333»' 
+rx .200,000,000,000,-^.142,857,142,857, 
+rx . hi, hi, hi, hi, - rx. 090, 909, 090, 909, 
+rx .07 6, 9 23, o 7 6, 923, -rx. 066, 666, 666, 666, 
+rx .058, 8 23, 5 29, 41 1, -rx. 05 2, 631, 578, 947, 
u +rx .047, 619, 047, 619, -rx. 043, 478, 260, 869, j 
X ? 
= r x 1.494,476,765,064, -rx .729,876,073,581, 
= rx .764,600,691,483. 
Having thus found the value of the firft twelve terms 
of the feries /-^ r +— -•—«-+ -^r- + &c. to be 
rx .764,600,691,483, we muft apply the differential 
feries to the difcovery of the value of the remaining 
part of this feries, which is the feries 
r* e 1 t" r 3 /» Qr 
25r l+ 27 r 14 29r* 8 3ir 3 ° + 33r 31 3S'' 3+ "^" 37>" 36 cCC.eid 
t * 
Jinitum . Now this feries is equal to the produdt of -r 4 into 
the feries 
it 1* 
t ro ,i 
+ 
>»* 
25 27 rr 29 3 4 3ir 6 33^ 35r‘° 37r xl 397- 
+ &c.or 
(putting x, as before, = to the product of p - 4 into the 
feries 
