and Infinite' Series '. 
445 
By the feries 
By the 2(3 fertes 
A = '3333333 
- — '■ 
B zr *0020406 
C — *0000330 
D = *0000007 
- 3333 66 3 -• io g- 
1*5229217 
,*0020413 - - log. 
3’3^99°68 
il - j/ ii£ . . 
4 121 
O*2088282 
4* - 3/512 
^ V 121 
0*2088282 
feries ££ — *5392500 
ferries == 4* *0033016 
3 ‘ 5 i8 7350 
X = -5- *2712508 
' c. o 
X == — *2712508' 
r zr — *2679492 the leaft root 
r = *2679492 the fame root* 
Agreeing with the fame root found in Ex. 4. Art. x Q6. 
131. But the fame root has been found to be 
- 2 + %/ 3 in Art. 59, and hence we obtain the fums of 
thefe two particular feries, thus, 
^13-^9 + 2 — -/i 
8 
^13 — ^9— 2 + 
8 
I 2 1 = — + 
2 . £ . 8 * 1 1 . 2 4 
3 . 6 , 9 .. 12 , 15 . II' 
+ See* 
V^I2I - 
2 . $ . a 2 
. 5 . 8 . n . 14 . 17 . 
3.6.9. 11 1 3.6.9. 12 . 15 * 18 „ 2i.11* 
132. Alfo by taking the fum and difference of thefe 
two, we have 
=A + Isltl t + • + See. 
4 v - 3 3. .6.9.II 3.6.9.12. 15. . II* 
^ 3 
?/*,,_ 1 2 • 5 - ? 1 . 2.5.8.11 
V 121 - — + ————— 
8tc. 
4 r 3 3.6.9.11- 3 . 6 .9 . 12 . 15 . 11 4 
And this laft expreffion agrees with what was found in 
Art. iq 8. 
JNT n n 2 
133. Ex. 
