the Value of a slowly converging Series. 195 
10. There now remains, of the proposed series, x ,4 x : —• + 
5 ^4 A’2'8 r 32. 
- + — + ~“+ — + — + & c - ad infinitum, = x 1 '* x 
the sum of these two series. 
X + 
3.8 
. A 8 
.r 1 * 
~I6 
J , 1 , 
.l’* 4 
XI 
12 > 
13 
14 ' 
*5 
1 6 * 
* T* 
2 X 3 
12 
* 
+ 
2 .r IC 
H 
* 
+ 
2 .t 4 4 
16 
, &c. 
Here, likewise, the value of the series which has the signs -f 
and — alternately, is easily obtained by a swiftly converging 
series, the terms of which are set down here below, the decimal 
value of being used in the calculation, for the 
sake of facility. 
P 
Q 
v 
X 
Y 
II 
P, 
12 
L 
2 Q- 
*3 
3R 
14 
4S 
15 
- n 
5 T 
16 
6U 
17 
7 V 
18 
8W 
19 
9 X 
x 39617*1 7287,6 = 0*00118,90306,0 
x 0*39617,17287,6 = 0*00007,24708,2 
x 0*39617,17287,6 = 0*00000,61523,3 
x 0*39617,17287,6 = 0*00000,06499,7 
x 0*39617,17287,6 = 0*00000,00112,5 
x 0*39617,17287,6 = 0.00000,00017,3 
x 0.39617,17287,6 = 0*00000,00002,9 
ft 
20 x 0 '39^ 1 7 j 1 7 2 ^7>^ = 0*00000,00000,5 
0*03728,40092,2 = y. 
The sum of these terms is 
C c 2 
