■ of Infinite Series* g 1 3 
fum of the fame feries ad infinitum , minus the fum of all the terms 
from 4- *= (If x + r = n) A — — — — — 4* — - — — ~ 7 4* &c. in 
the fame manner ~ + -4 -f &c. . . -r;B — — — — 4- -~ G 
2 3 3 3 272 272 3 4« 4 1272 
— JL.4-&C. ; and fo on for the other feriefes ; hence, by fub- 
1 ,I2« 8 ' 
flitution, and adding unity to each fide, we have hyp. log. 
2C'+ I — — &c. 4 — 4- 4--= 4* — 
* ^ * 272 1272 2n 3 I2C 
372° 1 2O/2 4 572 
I 41 
r 
25272 
+ -= + 
31 
4“ &c« tz T-+ \ 4~ § 4* \ 4* &c* • • • — 5 but 1 — \ A — 
X 
772' 24022 
= ,577215664901 ; hence i + i 4- f + &c. 
• ’ • ~ =hyp - log ' X + ’ 577 Z 1 5 66 49° J + i + A* p + 
3* 
I 2072 
[ , i , 4 T , 1 
■Hr — r H "6 + — 7 
L 5* 2 5^ 7» 
31 
See# 
•-6 
240^2 
Ex. 1. Let # = iooco ; then 
hyp. log. 10000=9,2 1 034037197 
conft. quant. = ,577215664901 
,000049995000 
1 
272 
==±2 ,000000004166 
1272" 
therefore the Turn required =9,787606036043 
Ex. 2. Let * = 10000000 ; then 
hyp. log. ioooooog = 16,118095650958 
conft. quant. = ,577215664901 
dL= ,000000049999 
therefore the fum required =16,695311365858 
VoLe LXXXL 
T t 
PROF# 
