898 Summation of the flowly- converging 
the great magnitude of b , zb, 3 b, 4 b, 5 b, 6 b, 7 b, See. in 
comparifon of 1,- will be almoft equal to (though fome- 
what greater than) 1 + ~ ax+ —^xx + ^cx^ + ~da: 4 + 
Kb (. 6b _ >]b o n I . 4 , 
4- ~ b FX + fj"b GX * €b HX ' ^ C * ° r 1 + 1 + + |-Ctf 3 + 
|d ^ 4 + |ea; s + 4 -f.y 6 + |ga ? 7 + -5-ha ; 8 + &c. or i+|xi x ‘ v 
*r J O _ 7 D 0 
TjX 7 x I X XX + T X -f X 7 X I X AT 3 4 -J-X — X 7X 7 X I x^ 4 + &C 8 
z b 3 z b ^ l z b 
I 1 I I T 0 1 T 4 O X ** 
or I + £ A?+ j x j * J-x ^ x y # 4 + &C. or I 4 - j + 
+ y + J + 7 + £ + 7 + Si +&c * Therefore, multiplying 
j XX 
both lides by b, we fhallhave b x ; nearly = b + x + — 
I —ATI 
+ j + j + j ■+ £ + y + y+Scc.; and, fubtrading b from 
both Tides, x+~- + - + - + -- + i + v + T + &c. nearly 
’234567s 
T - that is, the propofed feries 
= < 9 x 
£=£x L 
1 — xi~r 
^ + T + y + 7 + y + &c - win be nearly equal to 
b x f — ^-1 r - b. We muft therefore firft fubtradt x from 
1 , and then divide 1 by the remainder, which will give 
us a quotient equal to And, having found 
this quotient, we muft extract its £th, or 
1, 000, 000, 000, oooth, root, and multiply the faid root 
by b, or 1,000,000,000,000; and, laftly, from the pro- 
duct we muft fubtradt b, or 1,000,000,000,000: and 
the 
