312 
Mr. Vince on the Sums 
PROP. XIV. 
See, 
To find the fium of the infinite f cries 
The general term, by writing 2, 3, 4 , &c. for x, is 
4- _1 — &c. ; hence the fum = | A - JB -f T C 
AT . 2X+1 2 * 4 * 
— &c. — (by Prop. 13.) | - hyp. log. 4 
PROP. XV, 
T o find the fium of i -f - + - -f 1° ~ • 
The hyp. log. -i- = I + — + i. +_L + &c. ; confequently 
!iyp. log 
* 1 
x — - I 2* 
_ . J L - &c. = - ; hence, if we write 
2 ov3 v4 
2,3,4,&c. for#, vvehave hyp. log. j + hyp. log. ~ + &c. 
hyp. log. — x — + -T + &c ~r 
jsr t> x _j 223 * 
±x i +J. +&C 
3 23 3 * * 3 
i-x4+4 + &c. 
4 2 4 * * * * * 3 
— &c. &c. &C. 
_i - ,2 
1 + 1 + I+ &C but hyp. log. f + h 7 P- lo S- f '+] 
2 3 4 * 
hyp. log.4 + &c hyp. log. ~ = hyp. log. i x f x ± x; 
&c — = hyp. log. x; alfo 4 + 4 4- &c the 
X mmm I O 
y fum 
