of Infinite Series. 
307 
— 4- \ ; hence, by 
general term will be 2 , , 
writing ?, 3, 4, &c. for x, we have the fum = - ,576674037469 
+ A = ,06826002938. 
If n be negative, then === 
n n 2 xn 
x a .ax"-m “ x ~ m ox ax 
- &c. 
m 
Ex. i» To find the fum of - — 7 t— + 
4 - &c. 
1.2.3 2 • 3 • 4 3 - 4*5 
1 _ 1 _ 1 _ 1 . 
2 , ? 
Here the general term is — t 2 , , 
now, by writing 2, 3, 4# & c * ^ or x > ^ ie ^ ura ^ er * es 
whofe general term is is = fi by Prop. 2. ; hence the fum 
required = ^ — A. 
Ex. 2. Let the given feries be 775*7^ + 3 /*, ; ^ + | 
Sec. Here the general term is the fame as before, writing 2, 
4, 6, &c. for x ; and, by Prop. 2. the fum of the feries whofe 
general term is is = hence the fum= - — A". 
Ex. 3. In like manner the fum of the feries — ~~ ■ 4 - 
&c. ~ ,221689395104 — 6. 
2 . 3 + . 4 3 • 4 4 • 5 
Ex. 4. To find the fum of + BT^TTo + IJTTFEl^ 
; + &c. Here the general term 
■ r # 
'a — JL; but the fum of the feries whofe general term is 
1 x*~l X* 
_L_ is = ,086662976264; hence the fum required =. 
SC — ■ I 
,08 6 6629 7 6 2 64 — C. 
S f 2 
P K 0 P. 
