398 | . Dr. Wanine on the 

we Be Eb ye —2 41 Be, ing aia a 
The fame principle may be applied to find the fum of any | 
feries of the abovementioned fort, in whofe denominator are 
contained other factors, ra+g, rz+g+r, &c. &c.5 or 2rz+g, 
arzt+g+r, 2re+g¢+2r, bc. Like propofitions may be de- 
duced from feriefes, in which r and 7’, &c. and the faGors 
re+eand r’z+¢, &c. denote different quantities. 
10. An apparently more general method may be given from 
affluming a feries or feriefes as before ; and adding every two, 
three, four, &c. (”) fucceflive terms together for terms of a 
new feries beginning from the firft, fecond, third, &c. nh 
term. and in general adding together two, three, &c. 2 fuc~ 
ceflive general terms; and in their {um writing for 2 the diftance 
from the firft term ef the feries 2244, 3244, &c. we+a;3 
there will refult the general term of a feries not to be found 
from the above-mentioned addition. | 
Ex. Let the feries aflumed be 14+43+23+4+1i1+&c. im injini- 
tum, of which the general term beginning from the firft 1s 
= add three fucceflive general terms a ee +o 
> & 
22 -L19Z+1I : : , 
= ERS e in this term for = write 32, and there 
+3 

292° + 362411 
begining is inftituted from the fecond or third term of 
32° + 182426 
In the fame manner, if the 
the given feries, the terms refulting will be 
B39. St4- S+5 
bofale 27% +5424 26 anette 47 
and —— 
3%+2 + 32+3 + 3344 3243+ 3244+ 3245 
In thefe terms for % write 3%, and there 
o 
