| 
Summation of Sertes. 393 
— its dimenfions in the denominator by unity, then the in- 
tegral of the general term cannot be expretied by a finite alge- 
braical function of x. If the number of terms to be added be 
infinite, it is well known that the fum in this cafe will be 
infinite. 
‘ft may be obferved, that in finding the fum of a feries, 
whofe general term is given, all common divifors of the nume- 
rator and denominator mutt be rejected, otherwife feriefes may 
appear difficult to be fummed, which are very eafy: for exam- 
. : I 4 9 . 
Ce be TPs 4k 5 0. 1 en H Oy Oe) EO) pte 
2 
# heat (144g dt Be), whofe 
ZH. 
general term is Se Tg A seh 2 ee S 
; and by affuming, as 
s before taught, 32+ Re ix 32+ 2 xa for the fum fought ; 


and finding its general term 32+ 1 x 32+4 %3%+2. x! 
32+5 x18%+4+1%xa, which equating to the general term 
given, there refults 18a=1, and the fum fought = = 
i8 
I 
B24+1. 3%+2- 
he) Wetwthe fers be ol eee 
Epa Ziv. Siskin 5 Sis Oe Pure ag 
S5 140 Ligvan ae 
9-10-11 Ee ieee) ie Sine a ae ve oes ae 

I 
a &c.), of which by general term is ; Be 
—_—_—___ ; Ao confequently the fum deduced is — x’ 
ett. 4+ , : ae 
i I 
4 4241) | | 
Thefe are feriefes given by Mr. De Moivre, and efteemed 
by Dr. Tay tor altioris indaginis. 
VoL. LXXIV. Ff £€ i Some 

