of Infinite Series , 
Sox 
Into — , — , &c. ; hence the fum of each of thefe feries 
m m l nr 
being known from the tables, the fum of the given feries will 
be found. 
Ex. i. Let — — be the general term ; now 
I ° 
1 
x 4- i x 1 
T-T -f &c. ; hence if for x we write 2, 3, 4, &c. we have 
** AT 8 
L .+ 1 + - 1 + -L + &c. = A-C + E-G+ &c. = (by Tab. 1.) 
5 10 17 26 
,5766740374 69. 
Ex. 2. Let — L be the general term; then, by the fame 
I 
method of proceeding, — + f-d'~ + r: + = A 4- C 4- E 4- 
&c. = (by Prop, i.) ^ • 
Cor. Becaufe ~ 4 - + 4 + & c - = | x 1 4 - 4 - 7 4 - & c * = (as 
8 2 A a.8 8 a o 
i 4 - I 4- i +&c. is the reciprocal of the figurative numbers of 
3 6 
the fecond order") *- X2 = - ; therefore - +--+ — + &c. = - . 
'8 4 3 b 35 2 
Alfo, as — L---L+J- + 4 +&c. ; if we write 2, 4, 6, &c. for 
.AT — I X 
x, we have - + - + -+ &C,- (by Tab. 3.) A"~j-C -E lh -f- 
3 »5 3S 
&c. = - ; but, by Prop. 1 . A." 4- B" + C" + D" + &c. = hyp. log. 
2 , 
2; hence B"+D" + F' / +&c.= 4- hyp. log. 2. 
Ex. 3. Let the general term be = A 4. A 4. A. 4. &c., and, 
by writing 2, 3, 4, &c. for r, we have J- + ^ + &c, = 
B + E + H + &c.= ,221 6893.95 1 04. 
Ex» 
