922 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

(517-8) are verified, whence it follows that the limited expansions
 derived in the case of the general model for the different
quantities, and given in § 240, may be used.

518. Secondly, since n >, it follows from (512-12),
(512-13) and (512-14) that

1 Ew'w,, Ac Into,
5181) 2 Eros 0 ro]

Assume that

(518-2) w, =0 for n-1>= 9p

so that the sums only cover p terms. Assuming further that the
nw, _, are never-increasing, then applying the Tchebicheff inequality
 (1)

(518-3)

2 15 JF
n° w 2X n 2 nw.
nS sel n=1 n-1

whence

(518-4)

A

I En
p En a,

i.e.

(518-5,

N

1

13
nm

() BRONSTEIN-SEMENDJAJEW, 0d. cit., D. I35.

T11] Allais - pag. 226