432

CAPUT- V.

Quia est % — (ix-i) 3 — Bx 3 — i2x* -f-£.r_i. cr i t;szdx — 4 ^r 3 < ( ■ 3 x 2 -x ; 24^»—24^-j- 6;

</</ i 5 d 3 z

= 48* — 24 ; :=: 48 ; sequentia euanescunt.

Quare erit S(2 ^-i) 3 ~2^ 4 —-*4jr 3 • 4 - 3 .r 2 —x

—I— 4-v 3 — 6 x 2 -4- 3*— ;

—}— 2X 2 <—-2X —-§-

, * - . - I

TT

hoc est S(2*w)* ZZ2.* 4 *— x 2 zz* 2 (2xx— 1). Sic eritposito x — 4 i-f-27-+-125-f-343 zz 16.31ZZ 496.

132. Ex hac inuenta generali expressione pro termi-no summatorio lponte sequitur ille terminus summatorius,quem superiori parte pro potestatibus numerorum natura-lium dedimus, cuiusque demonstrationem ibi tradere nonlicuerat. Quod si enim ponamus zzzx" y erit vtique

szdx zz —jr»-w : disserentialia vero ita se habebunt:

»+1

dzdxddzdx 2d 3 zdx 3d S zdx 5d 7 zdx 7

ZZ nx H ~ l

ZZ »(«-1) x n ~ 2

ZZ n (n — 1) (» — 2) x"-t

ZZ »(»— i)(«— 2 )(»— 3) (« — 4)

~»(n— 1).(«— 6 ).r "~7

&C.

Ex