% 
% 
the Value of a slowly converging Series. 197 
12. There now remains, of the proposed series, only x 48 
x : — b ~~ + + & c ‘ a d infinitum , the value of 
<y>i6 -32. -y48 
which, or of its equal, x 48 x : [■* — - — j — g — |- - — + &c. 
may easily be obtained without any transformation, since the 
powers of x 16 (== the powers of 0*18530,20188,9) decrease 
swifter than the powers of The numerical values of these 
terms are as below. 
4 
* r 
.z 31 
5 
x** 
6 
X 6 * 
7 
* 8 ° 
8 
9 
x 112 
10 
x 118 
1 1 
x 144 
12 
X ,6 ° 
' 13 
X ' 76 
H 
x I9Z 
1 
15 
0*04632,55047 
0*00686,73676 
0*00106,04476 
0*00016,84313 
0*00002,73093 
0*00000,44982 
0*00000,07502 
0*00000,01264 
0*00000,00215 
0*00000,00037 
0x0000,00006 
0 * 00000,00001 
The sum of these terms is 0*05445,44611' = F. 
