of Infinite Series. 
3 ! S 
?|4 hyp. log. ^+&c. = B+fE+fH-f &c. = ,211466250444.; 
or hyp. log. — x 32 x p x &c. = ,21 1466250444; hence x 
J r 0 7 20 03 7 
?1 x ^ x &c.= 1,627295, &c. 
26 63 
Hence we may find the value of fuch a quantity, fuppofing 
the number of fa&ors to be finite. 
Ex. To find the value of - x ± x - x &c to - 2 ±- . 
13 5 7 .X 1 
Here the general term being w e have - - —v— = - 
- &c. ; hence hyp. log. 22 — = — j- 
J 1 0 '2# — I X . 2* 
X * 
.2 
AT 
2 x* 4.T 3 8 a- 4 i 6a- 5 
1 . 1 1 
1 4- - J I 1 &c.. Now write 2, 3, 4, &c. 
a . 4** ' 3 . 8**^4 . i6x 4 1 
for x, and we have the hyp. log. i- x — x - x &c 
3 5 7 
2-y 
2*— 1 2 
1 
1 x , 1 , 1 | 1 
SS X “ Hr- — Hp •*••• — 
2*3*4 * 
1 , 1 1 1 , 
X — - 4 + 
2.4 3 4 
+ _L,x *,-f ~ + 4 + 
78 '' a* • 3 3 4 3 
+ &c. 
&c. 
I 
&c. 
X 
But, by Prop. 15. ± x i + | + ± + 7 = fhyp. log. 
- ,21 1392167549 + 7 + ^ + 4 " + - i 4 -i- -r-« + 4 tt* + &c - 5 
d fo _l_xi + T + 
4 w i “24^ 6^ 240a* io« 5 504^ 
1 
2 . 4 
n 
2 rc 2 6 tz 3 30/2* 
■ X I I i __ x p x ^ x ^ I | 
&C. and — -gX 7+7 + • • * x ^ 
I2» v 
~&c., and fo on for the other feriefes ; hence, byfubftitu- 
T t 2 Sion, 
