the Value of a slowly converging Series. J91 
^ = 0-05294,1 1764,71 
X Z 
— = 0*04500,00000,00 
3 
^ = 0-03836,84210,53 
— = 0*03280,50000,00 
^ = 0*02811,85714,29 
~ = 0*02415,64090,91 
^ = 0*02079,55173,91 
^ = 0*01793,61337,50 
The sum is 0*26012,12291,85 = C. 
We may now quickly find the sum of the first twenty-four 
terms of the series proposed, by two multiplications by x\ and 
two additions, as was pointed out in the former part of this 
article; but, since the labour of these two separate multipli- 
cations may be saved, I shall now proceed to compute the va- 
lue of the remaining terms of the proposed series. 
a 'T>u • • , x 7,5 . x 26 . x 27 . x 28 x 29 
6. 1 he remaining terms are -f- -f- 
*30 
-| 1- &c . ad infinitum, which, being disposed according to 
30 
the form mentioned in Art. 2, are evidently equal to x 24 x these 
f * 
two series 25 
I * 
L * 
+ 
2 x * 
26 
27 
* + 
28 
2X* 
+ 
X s X nr> 

29 30 9 
the value of the first of which is very easily attainable, in the 
manner shewn above, in Art. 4. The arithmetical work will 
stand thus ; 
