invefiigating the Sums of infinite Series. 40 1 
middle factors; and when the number of factors be odd, the 
numerator will be equal to the middle factor, and confequently 
will take it out of the denominator, and leave a fcries whofe 
numerators are unity, and whofe denominators want the mid- 
dle faffor. 
The method of fummation of feries here made ufe of may 
alfo be applied in invefiigating the fums of a great variety of 
other feries ; but as a further application of this method would 
carry us beyond the limits to which this paper muft be con- 
fined, I (hall re-affume the fubject at fome future opportunity, 
and proceed immediately to the fecond parti 
PART IL 
PROP. 
To find the fum of the infinite feries - — 
n-'-m n + rm 
+ 
1 - _ _p s -p &c. when the lafi difi 
.... n-J-r-p I • m n -r 27/1 ... . »-pr+ 2 . r/i 
ferences of the numerators become equal to nothing. 
Afl ame a -p nb -p n . n -p m . c -\-n . n *P n% • n -p 2 in • d -r ^ 
any number (r) of terms ; then, if for n we write n + m,n+ zm* 
n+ 3m, &c. fucceffively, there will refult a feries of quantities 
Vol. LXXII. G g g whofe 
