3 02 Mr. Vince on the Sums 
Ex. 4, Let the general term be — ! — = _L + _L + i 4. 
3^-2 3* 4 9* 1 » 
and, by writing 2. 3 4, &c. for x, &c. we have — + -1. +_L + & c 
46 241- 766 ^ 
L c + ?G + ^L + &c. = ,02838 252252. 
Ex. 5. To find the fum of the feries I-J- + -L L 4. 
rr 9 20 ~ 65 ] 24 + * 
If we write 2, 3, 4, — 5. for ar, the general term will 
be ^h = i~i + i ~^ +kc - N °w, b y writing 2, -3, 4, 
“5* for x, the fenefes of which - s , - t , &c. are the ge- 
neral terms, will be alternately 4- and - * , and therefore their 
iums will be found 111 Gab* 2. and the leneles of which 
are the general terms will have their terms all +, 
and therefore their fums will be found in Tab. x. Hence 
the fum required = b + h-+o+ Sec. -E-L-R- &c. => 
,082800931803. 
PROP. III. 
To find the fum of the fums of the reciprocals of the odd 
powers in Tab. 2. 
By divifion L— s JL + + 4 + 4 + &c. 5 hence by writ- 
x—ixx**** J 
Ing 2 — 3, 4? S> fums of the feriefesof which 
jf» l > &c are the general terms, may be found by Tab. 2. 
and the other fums by Tab. 1. ; hence — — -J_ 4- _JL + & c 
1.2 3.4 3.6 
= A + C + £ + &c. + 3 + J+/4-&c, 5 but — h--j — 1 — | — 1 — 4 . 
1 • 2 3.45.6 
&c. 
