276 NEW SERIES for the 
where T(m), T(m+1), T(m+2), &c. denote the terms whofe 
places in the feries are exprefled by the numbers m, m+1, m+2, 
&c. Then, becaufe 
T(m42)< ; Tom4n)s 
T(m+3) < 7 Ton) 
Tents < 5 Timgar 
RCs ri 
We have 
T(m+2) + T(mt3) + Tmga) , &e. < i (Tent) 
+ T(m42) + T(m+3) +, &c.) 
‘That is, putting S for T(m42) + T(m+3) + T(m44) +, &e. or 
for the fum of.all the terms after T(m41), 
I 
Ss <5 (Tom+1) + S), and hence 3 w= 7 T(m+1),&S aa T(m+1): 
Thus it appears, that the fum of all the terms of the feries fol.- 
lowing any term after the firft, is lefs than the third part of 
that term. 
11. AGAIN, from what has been faid in Article 9., we have 
Tim+2)> Bane T(m+1), and therefore pitee) > Ems) 
(m1) Tq)’ 
F Tim ) Tom 2) m T 
g lay t+? 5 qd = (m+4) zieba), 
and fimilarly T(m+z) at T(m+ 1) ii T(m43) ‘ Tom42)° 
and 
