QUADRATURE of the CONIC SECTIONS, &c. 277 

 and fo on. From which it follows, that 



T 0»+*) > tv~V T^ + Oi 



1 (m) 

 T 1 / -^ -^ ('" + * ) ""p -v 



*(»+3.) > TV > 1 ('" + 2)> 



••■Cm) 

 &C 



Hence, taking the fum of the quantities on each fide of the 

 fign > , and putting S for 



T( ra + 2) + T( CT + 3 ) + T(m + 4 ) "b &c. 

 we get 



Therefore S — %±llS > Sp^i and confequently by re- 



J- (?») A (m) 



duclion, 



1(») I(m+i) 



from which it appears, that the fum of all the terms following 

 any affigned term after the third, is greater than a third pro- 

 portional to the difference of the two terms immediately be- 

 fore it and the latter of the two. But fince this limit will not 



differ much from the former, which is - T( m '+i), it may be 

 more conveniently expreffed thus, 



3 3( T («0 — T £* + 0) 



Mm 2 which 



