Mr . Vince on the Sums 
PROP* V. 
To find the fum of the Infinite feries — -f~ + — + — -f-_L + 
l S 40 #5 156 259 
&C. 
In this feries the fourth differences of the denominators 
= 0; therefore the general term muff be repfefented by 
; wr * te therefore 2, 3, 4, &c. for a?, and we have 
8/7 + \h + 2c + d = 1 5, 27/7 + 9^ + 3<; + d ~ 40, 64/7 +1 6^ + 4^ 
fid =- 85, 125/7 + 25^ + 3^ + ^= 1 } 6 ; lienee = 1, c = 1 , 
d~i 9 and the general term is - 1 rz 1 l + JL — _L • 
■+■ x -f- I A 2 a 4 A 17 A* 
&c. ; hence the fum = B — C + F-G-j-K — L + &c. =. 
242700.1 65. 
PROP-. VI* 
the fum of 1 + A + _i. + & c . ^ /«£ 
The general term = -A + & c .; hence, by 
writing 2, 3, 4, &c. for «, we have the fum = B — 2D4-3F 
L“ &c = ,147115771469. 
In like manner A + A+ A + &c. = B + 2D + 3F + &C. ==’ 
*312498999865. 
PROP. 
