330 
no b 
IV. Lim }, =0 and either }, > 0, orthe series > —% converges 
— x n==1 nq 
for an unlimited number of integers g and the sum of this series 
is different from zero. In the latter supposition we have 
n= Ong 3) 
Lim (1—2) Ne) — = Z, 
mnd | n==1 1G 
V. 6,20 and moreover 
) l 
Lim — [both + baga +... + dng pi] = 0 
n— Po 7 
(SON reeel) 
for an unlimited number of integers q. 
1) By a totally different method FrRANcK deduced this formula in his paper: ~ 
Sur la théorie des séries. Math. Annalen, Bd. 52, 1899, p. 529. 
