and Infinite Series. • 431 
ro6. Ex. 4. In the equation x'= - icx - 4, we have 
a - - 5, b = 2, and c-s/^ + a 1 = V- 121 = 1 1\/~ 1, 
imaginary and greater than b, which belongs to the fame 
feries as the laft 2 examples, but changing the lign 
where the odd powers of the negative-quantity c z is con- 
cerned, as in Art. 98. 
Now l - — — — — and 
C 11 12 X 
4 ,= = Then 
yc* 121 > I 2 I 
A = 
G = 
3 
8 ■ i i** 
12 . 
= * 33-33333 
3 = 330 
+ *3333663 
— ’0020413 
2 . cl z ' s 
B ~ 6 rf? A “ *0020400 
14 . 17^ 
D = TiblA c = 7 
•0020413. 
the feries =*3313250 - log. 1*5202543 
s/~ - - - 2*9077982 
the leaft root = - ’2679492 - - T , 42.8o525, 
107. To find the other roots by this method, we 
rauft fum the feries tyc . v 3 x : 1 + — —7 - &c. And 
3 .DC 
as the terms of it are found by multiplying the terms a, 
b, c, 8ec. of the former by 4, 4, ff, —j Sec. refpe£tive~ 
Ly, we fhall therefore have 
