* 
39° Dr. WARING on the a 
er eer ree pera ora 
ted whi pet i &e xwtf xatfriruxtfy+2.., x. 
a ee ix &c. =D, where z, 2’, oe Sc. 5) ag &c. are’ 
a tebe "shez bP ++ 8c. : 
D 
=T”’; then, if the dimenfions of = in the numerator be 
lefs than its dimenfions in the denominator, will ey A = 
& a al! Pie fa 8. N a is 
(2a Bien Cor ani Fea sy GHP 
ge Sree 0 
pire in anal there will be included all terms of the formule, 
whole numbers; and the general term 1s | 
+ &c.) + &c; 


A(ayesie mett) | 
(ste? - (ztet1)° - . Gee 
Batre! Gt!) Sts 
(tf)? + @tftnh ++. @Hftit ” 
C Cetetutiyha(tete?) ge 
Ceteteyh > (etebebiyh es (abete diy 7 
where A, B, C, &c. a, «’, &c. B, B’, &c. y, 6, &c. denote in= 
variable quantities; and p, pf’, p’’, &c. are whole numbers not 
greater than =, e, 7’, &c. refpectively; andz, 7’, 7’, &c. ate 
whole numbers not greater thanz=1, m—1, &c. 
If all the quantities @, a’, «'’, &c. , B’, B”’, &e. &c. are 
=o, the fum of the feries can be expreffed in finite terms of 
the quantity z, otherwife not; and alfo if 4 be lefs than the 
dimenfions of sin the denominator by two or more, then will 
e+@6+&c.=0, otherwife the fum would be infinite. | 
From 7+ 7’ +e+&c.=1 independent fums of infinite fe-— 
tiefes of this kind can be deduced the fums of all infinite 
feriefes of the fame kind, 
2 Thigh 

