§fi Infinite Series. 
3 11 
/ 
PROP. XII*. 
To find the fum of - 
finitum . 
2 2 - 3 " 
j 1 — , + 1 — 5 -f &c s ad in - 
r 2-3 - 4 3 3-4 2 -5 3 ^ 
Here the general term, by writing 2 
- 1 -£.+ -£ + 
ft T * 8 * 
* — I .A 2 . AT — j— I 
12 
AT 11 
, 3, 4, &c. for x 9 is 
- i ~ _ &c. ; confe- 
12. * 
quently the fum = E — 2F4-4G — 6H — 9I — 12K + &c. — 
,010370898482. 
PROP. XIII. 
To find the fum of j A -|B + ^C — &c. ad infinitum. 
The hvp. log. 2 = 1— — + — — - +-7 — &C- = 1 + - -f ^ +•■ 
" r 6 2345 35 
&c. - — — - &c. ; hence 2 x hvp. log. 2, or hyp. log. 4, 
246 . 
= JL 4- JL + JL j- See. — 1 — — — — &c. Now, by divifion, 
135 2 3 
~ 1 — = i - — z + - 4 +&c, ; hence, by writing z, 3, 4, &e. 
2 A 4* I A* 2 A or 
for x, we have (after tranfpofition) ~ + - +&c. — — — — — 
— &c. = — § A + J B — -J-C + &c hence, by adding equal quan- 
tities to each fide, we have — + - + - +&c. — - — 
13 5 234 
&c. = - — 4 A + |B — 'C 4-&c., confequently l A — |B+,G — 
3 
&c. = - - — — - &c. + 1 + l + - 1 + &c. = - - hyp.l0g.4v 
3135 2 3 3 
PROP* 
