lim — e Q : . * e Q

Ur 4--I

63. V £ Q f Z,^+, . a , 6 , (6 — a) S Q . ^ S (a- 6) f Z ^, : r S Z ^ . Or . — ^ =

Vr+i(^rVr-^l) 1 ,W,^^, UA ^ V%, ^ ^ /^^n+i ^i^

Vr b \Vrn+i ^i' * « Wm+l ^i'

64. a , 6 , (6— a) e Q . -y e Q f N . 4/ s (a- &) f N . 2^' zi e Q : r e N . Or . ^^* =-

^-î-— : . lim — £ Q .

V, Vn

\ Vn vj 1 a \ Vi vj

§ 4. (Q f N) decr.

1. w , v £ (Q f N) decr . 2 w^ £ Q . 2 1?^ = x . 9 £ (N f N) cresc . 7* e :^ : r £ N . Or . t^.^^./ v^^ > 7i .-. . 00 £ lim (Çrt^-i — 9j .

§ 4. 1. GiUDiOE. Giornale Battaglini, a. 1890, pag. 287.

VIIL — § 4. 96

, 2. i4£(QfN)decr.Xe{NfN)cresc.maxlim^--^<1.2tt^eQ.o.2!'

3. w £ (Q f N) decr . X s (N f N) cresc . min lim r-^ > . 2 1*^ = oo . o .

4. w e (Q f N) decr . a e N . o : 2 w^ e Q . = . 2^ a** t^^n e Q .

5. i; e (Q f N) decr . 2 v^ e Q . w^ = t;^ — Vg . Wg = 2 (v^ — Vg) . W3 == 3

K-^4) ^•2r^ = 2, - -hS^ -+23 - +... = 2^ «.

€. «e(Qf N)de<Hr.inax lim «M«> 0.0.2 M„ = 00. fPP^]

7. » . : 2. w^ g Q . = . lim nun, = 0.2^ n (un — t^n-i) £ Q .

9. i^£QfN.2î*^£Q.-r-,aw£(Q f N) decr . lim Xn === 00 . max lim an

(>^a — Xn~i) £ Q . . lim X,» «H t*n = .

[Hp .0.2 (X,» — Xn-i) a., t^/i £ Q . lim r-^= , (Xm+i— X,„) a,«+i

WmH-l-+-»..H-(X«+rt — >^n+«— 1) ^ïA-k-n ^/n-hn ^ X^+n (1 — -^ )

a^+H w^+n : §2 P3 . . Ths.]

10. i^ £ Q f N : w £ N . o« . ?iW/» >(7i -f- 1) Mw+i : max lim nun log w>0 . o .

lu^^oo. [§4P9.§2P46]

.11. 1^ £ Q f N : 71 £ N . Oa . nUn log 71 > (il -h- 1) î^rt+i log (tih- 1) : max lim

nu.i log 71 log* 7i>0.o.2î*^=oo. [ » ]

12. t^ £ Q f N : 71 £ N . 0,t . 7^^^ log 7l 10g*?l Xn -h 1) Wn+l log (71 4- 1) log*

(ri -h 1) : max lim nun log n log* 7i log^ 7i>0.o.2w^ =oo.

13. 1^ £ Q f N . 2 w^ £ Q : 71 £ N . On . nun log n log* 7l ... log"' TI > (7l -h 1)

Wn+1 log (71 -h 1) ... log*"* (7H-1) . . lim nUn log n log* 7i ... log**»-*-^

2, 3. DiNi. Annali Università Toscaney a. 1867, pag. 78-80. 4. Cauchy. -47iaZ. ^Z^., pag. 135.

« 1 , U i-hl — U,i

14.. uz (Q f N) cresc . d s Q f N . 2. ^-~ = oo . max lira — zQ.o

15. uz(Q f N) cres . c e Q f N . 2^° — s Q . min lim ^^'*"^^~"^" s Q . o .

Un-i'i — Un * 1