C 760 ] 
Turn of all the terms fo taken, will be truly obtained 
by fubftituting px, qx, rx, sx, &c. fucceffively for at, 
in the given value of S, and then dividing t'he fum 
of all the quantities thence arifing by the given 
number n. 
The fame method of folution holds equally, when, 
in taking every n rl1 term of the feries, the operation 
begins at fome term after the firft. For all the terms 
preceding that may be tranfpofed, and the whole 
equation divided by the power of x in the firft of the 
remaining terms; and then the fum of every 
term (beginning at the firft) will be found by the 
preceding directions ; which fum, multiplied by the 
power of x that before divided, will evidently give 
the true value required to be determined. Thus, for 
example, let it be required to find the fum of every 
third term of the given feries a-\- hx ft- c x z ft- dx l 
ex'*, &c. (= S Jj beginning with ex' 1 . Then, by 
tranfpofing the two firft terms, and dividing the whole 
by x~, we fhall have c d x ex z -\rfx\ &c. = 
" a ~ -_. i (== S'). From whence having found the 
X X 
fum of every third term of the feries c ft- dx ft- e x x 
ft- fx l j &c. beginning at the firft (c), that fum, 
multiplied by x l , will manifeftly give the true value 
fought in the prefent cafe. 
And here it may be worth while to obferve, that 
all the terms preceding that at which the operation 
(in any cafe) begins, may (provided they exceed 
not in number the given interval n) be intirely dis- 
regarded. 
