.. finding the Value of an infinite Series , 8cc. 19 7. 
the feveral orders of differences of thofe numbers, be- 
ginning from the fecond term }. Now the values of 
thefe numbers, 1, }, }, j, -f, -f, 8 cc. and of their 
differences of the feveral fucceflive orders, beginning 
from the fecond term j, will, when expreffed in decimal: 
fractions, be as follows : ' 
1 is = 1.000,000,000,000; 
7 = • 3 ' 3 ' 3 V 333 > 333>333 >' 
j = .200,000,000,000; 
7 = .142,857,142,857; 
I = .III, XII, 111,711; 
TT = .090,909,090,909; 
it = .076,923,076,923; 
l^j = .066,666,666,666. 
The differences of thefe numbers, beginning from the 
fecond term, -333>333>333>33> are as follows; 
Firft differences. 
•I 33 > 333 > 333 > 333 ; 
.057,142,857,143; 
.03 1 , 746, 031, 746; 
.020,202,020,202; 
.013,986,013,986; 
.010,256,410,257; 
&c. 
Second differences. 
.076,190,476,190; 
.025,396,825,397; 
.011,544,011,544; 
.006,216,006,216; 
.003,729,603,729; 
&c. 
Third 
