. AO lir tia phan gi6c cfra g6c EAF
crrdi cimg (tinh tit' trtii ,tung phdi) khi biiu didn nl trong hA thap phon IIoi diil,sr
didn nl. trong hA thap phon. IIoi diil,sri (a,,)t,t|i n: 1,2,3,... cti phdi lir mot dti1, .sd ntin hodn kA ir mot ltic ndo do hrq, khr)ng ?
:
(Dr71'r,-., lu,,) gt.ti li tuun hodn kA tir ntot ltic ndo do nAu tin lr.ti ctic ,s'6 nguyAn tluong T t,it
lt{ soct cho o;q-=ct1 Vi > 1/ ).
Ldi gitii. (Theo ban Nguydn Thdnh Khang,
1 I Toan, THPT chuyOn Hing Vuong, Ph[ Tho). Trudc het ta c6 nhan x6t 4,, + 5,Vr e N*.
ThAt vQy ta c6 a, = l. Vdi n > 2 th\
nl=2oz.3dt...po' v6i a, e N vi 7r., ld songuyOn td (thri s). nguyOn td (thri s). Ta c6 lnf I n1 l rl "'=lr).lt ).Lr l. lnf I n1 I n1 'L;].1"].Lol* =d5 Do d5 nt:lQds.2dr-ds Z; (2, l0) = l.
Thdnh thit ani2 s a,, * 5.
Ta chfng minh bang phAn chrfng. GiA sii tdn taiT, N € N* sao cho a1*7.= ai. Yi>. N (1) D6 thdy tdn tai ft, / e N. du lm sao cho k > / > N vd 10k = 10/(modZ).
(Vi trong day 10N*r,10N*2,... phAi c6 hai sd
hang c6 c[ng sd du khi chia cho I).
Dod6 ai*rok_rot =ai,Yi>.N (2)Tac6 arot _r=a,or (vi 10r!=(1Ot'-l)!l0t), Tac6 arot _r=a,or (vi 10r!=(1Ot'-l)!l0t),
do d6 tU (2) vdi i =70k - I , suy ra
Arck )algk -;gt = Algk
algk -1gt
Q Az.tok
-tor -t : A21ok ..to7 , DOII
(2.10k -10/)! =(2.10k -10/ -1)l(2.10k -10/) vb chft sd kh6c 0 cuoi cilng (tinh tr) tr6i sang)
cia 2.10k - l0/ lh 9. Thdnh thir ta phAi c6
azrck-tot-r =5. Didu nhy mAu thuAn v6i nhAn
x6t ban ddu. Vay ddy sd (a,) kh6ng ld ddy so
tudn hohn kd tt mdt hic nlo d6. D
(Nnen xet. Ddy lI m6t b)i to6n hay vir tuong ddi kh6 nhung v6n c6 nhidu ban tham gia giAi vI giai dfng (c6 m6t sd ldi giiri hoi dli). C6c ban sau dAy c6 ldi giai tdt:
Hi Nam: Dinh Htiu Anh Khou, l0 chuy6n, THPT
chuyOn Bi6n Hda; Hi Ndi: Mai Anh Bdng, 1lT, THm
chuydn DHSP HI Noi; Thanh H6al. Ngrryin Attlt
Thdng, l1T, THFrf chuy€r.r Lam Sorr; Nghd An:
Nguydtr Num Attlt, THPT chuy€n Phan BOi ChAu, Vinhl
Quing Ngai: 7d Dinh Dtong,l2.Al, THP| DLic Phd; Cdn TIro: Ll D uiThdnlt,l lAl, THPT chuy6n Lli TuTrong.
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*B:ii T11/386. Cho n s.ti khong tit'n c4,u2,...,o,,
(r > 3) thod mtin ai + al + ...+ oi, =l .