TRACT 28-

AND INFINITE SERIES.

ICf

A =

8. Hi*

C = ■ ; -. - - B

12 . 15c*

*f

= *3333333= 330

+ -3333663- -0020413

B:

o ■

■3.

6.9c-*14 . IW' 18 , 21 «*

the series = -3313250 - -, 04

i 21

the least root ~ — -£679492 - -

loo

= -0020405= . 7

— *0020413

T5203543H- 90119 82T-4280525

107. To find the other roots by this method, we mustsum the series yc . + 3 x : 1 + ■ ~ „ — &c. And as the terms

' Y 3 . Go 2

of it are found by multiplying the terms A, B, c, &c, ofthe former, by -f-, f, 44 , *-*, &c, respectively, we shalltherefore have

« — f A .— 1 i

e = | B = 0-0036731 r = As. c = - -0000450

* — D = 8 I

+ [-0036739— 0000450

series =+ 1-0036289 ----- log. 0-0015732

, 3,11 ------- 0-3471309

V'S - -- -- -- 0-2385606

±3*8660254 ----- 0-5872647

£ the least root jwith a cotitr. sign J

+ 0-1339746

sum +4-0000000 greatest rootdiff. -8-7320508 middle root.

108. But the same 3 roots, found in Art. 59, are also 4,and —Q±v'3; which being compared with the series inthis example, we find