of Infinite Series* 
3 ° 9 
PROF. VII- 
T 9 find the Jam of + 5*7^ + Tf.if + &Cl ad 
The general term is . 1 + A-i- 4 6 + & c - » 
lienee, by writing 2, 3, 4, &c. for x r we have the fiun = 
G + 2L 4-3P4- &C.=, 009447690684. 
PROP. VIII. 
To find the fum of l3 . ^ . - p + a . ■ 3 3 i 4 + fTfTf + &c " 
inf* 
Here the general term is — * - -^=^3 ~ + t 3 + &£*• 
and hence the fum = H + 3K + 6M + &c.=, 004707148337, 
PROP. IX. 
To find the fum of the infinite feries 1- — -fi - ~ + &c» 
3 
being a feries of the reciprocal of the figurative numbers of the' 
order , having thefigns alternately + and — * 
This feries, by refolving two terms into one, becomes- 
— 4 s 4 1 — - 4-&c, whofe general term, by wri- 
1.2.33.4-5 5 • 6 • 7 & 
ting 2, 4, 6, &e. for x, is ===== — - — + 4 + t + ^ c ° 
confequently the fum = 4B // + 4D /; + d- &c. — (by Cor. 
Ex. 2. Prop. 2.) - 2 + 4 hyp. log. 2.. 
