
#00 | Dr. Warinc on the 4 . | 
Mr. Berwou.ir’ s addition, &e. can be applied to. feriefes‘of 
ai 
this cat F or example, let the given feries be 2 oe at, 
a «+ &c.=8. From:this feries ‘fubtraat the Woe feries di- 

2 : Te I I : oe 
minifhed: by m:-terms, 072, —— x" 4 gt 
wis i é-+m MEGA Basti ati 
1. &c. and there..rcmains:, “0 4 ee 
.-é@. m-be Ob cebpmep ors 
pes Miz 7 Pear ee ™ 4 f fe M 
ii eh aang eh a ed ak aaa x 0° 8c. for x” ‘write A, 
e+2.e+-m+2 e+3 .¢+m+3 ; 
then will the feries become “224. chmbinepia ae fe} 
-m+e Pris oot a 
ebmr2—et2A 2 ides w+ &. = - =f er, 
é+2.¢+m-+-2 e+3 -etm+ 3 e+ 
pri x oe @ @ OED Fo 
é+2 eé+m—I 
mtb eee, epee 
Let the ral erm be DN get Ei. Eee as oe 
h tga : SteeSteti.zZfet2..S+etu—i 


7. og bite Me spre b Lps: ze § / 
= (4+ 4+ +’) x*. Suppofe @ = er, 
yi Xs O-0k, «- &= Xa? s then. will the tum) ofieme 
above-mentioned feries be (#+’ + y +0 + &c.) x S-= 
/ Za Ys youl , 
(C 18's +0 + &c.) nan (> +0 ar: 
by thefe 

From the ‘fum of the “feries 1 — 
é ae e+ 
and the principles before delivered can be deduced the 
fum of any feries, w hofe general term 1s 
ax” tho” "4+&e. oy 
2B-+e. 2Z+e+ 1. 22+e42. 224Fe43X &K, 
3 
In like manner from the fum of the feriefes * a +2 rea 
ec 
, 6 0h Pe ve? 
fen oe ee Ste &c. can be 
J I) ease &t+i gt2 
deduced 

