infinite Series tf+^ + ^ + ^- + y + &c. 897 
of each of them, that is, than the fractions — > — 1 —•> — > 
^ y O M O w A Vi r 1 Vi 
the lefs is the proportion in which they exceed the latter 
fractions; infomuch that, if we go far enough in the 
feries, we may find terms in it whofe proportion to the 
correfponding terms in the feries i, |, |, ~ 3 1, See. 
fhall approach as near as we pleafe to a proportion of 
equality. And, by taking n of a very great magnitude 
in comparifon of m, we may even make the firft terms 
See. approach very nearly to an equality with the cor- 
refponding terms of the feries *, |, |, |, |, |, &c. which 
are the generating fradtions of the propofed feries 
= a billion, or the fquare of a million, which, to avoid 
the frequent repetition of fo many cyphers, we will call b. 
Then will or \ or — i— ,be 
let m be taken = 1, and n = 1,000,000,000,000, that is, 
= I + -£ AX + 
I I -j -b 
BXX + 
x -~ h X s + See. which, on account of 
Vol. LXVIII. 
S T 
the 
