. Ndu I'thuoc ung iD kh6ng chri aC hoac
Loigitii (Theo ban Ddng Anh Tudir, ll{2,
chuydn DHSP HA Ndi).
Ta chring minh bii tor{n tdng qu6t hon.
Cho 2n so'tlu.rc dttottg a1, a2, ..., a,, vd br, br,
..., b,, thda mdn d6ng thdi hai didu ki€n sau:
l\ bi<b,,, voi i= 1,2,..., l - 1.kk kk 2) Lo,<Lb, r,di k= 1,2,..., n i=l i=l Khi d6 Chr:rng ta c5
minh (l). Ap dung BDT Bunhiacovski
Do d6 ta chi cdn chfng minh
,,-t('r r \
='ila--l |n,*Ls,, (3)
A\b, b,*,)' b,,
Laics B, =i', = i lr-rL , *or
"-tb frlb, b,_,)' bk$1,$l-L - .Z-/ t $1,$l-L - .Z-/ t i=tAi i=t Di [:rl [t+l = [f r]' \i,, ) la bi ) \xb, ) (l) (2) I b d6 At =2o,. Vi 4 < B, nOn ta c6 l=l B, * <y ",-, [r-r],*lL=f L=n (4) 1b, b,*, ) ' bk A br Thhnh thft ti (3) vn (4) ta duoc ./ \ $o,-S[ I1,,'-+l L..=Ll , , l'', -L,
A b: ,-I \D, oit ) D,, i=t Di
V4y t2t duoc chring minh.
Ap dung vdi b,=,(i + 1) (i = 1, 2, ..., n) dttoc
$lr\q / - / I =r- I = n .a
-L
A o, A iti+t) rt+l rr +l
(Nlan x6t. 1) Trong ldi giAi ta da nhidu ldn su
dung phdp bien dcii Abel sau
n n-l
I ,,y, = | (xi - x;*1)y; i-r,r-))ri=l i=l i=l i=l
i
6 d6 tr,; =Zy, .
t=t
DKh6 nhitlu ban dA girii sai khi cho rdng
il
lalSn(n+1)
l=1
hodcchoring a;<,(i +l) (i= 1,2,...,n). 3) Ciic ban sau c6 ldi giai tot:
VInh Phric: Phing Dinlt Philc, l2Al, THPI chuy€n
Vinh Phric; Hh NOi: Trinh Ngoc Dtong, l0Al,
DHKHTN, DHQG Hn NQi; Thdi Binh: NguydnVdn
Thdnh, llA1, THPI chuyOn Th6i B)nh; QuAng Ninh: Pham Dirc Hanh, 10, THPT chuy0n Ha Long; Hrii Phdng: Dodn Minh Duy€n, 1l To6n, THPT NK
Trdn Phri; Quing Tri NguyAn Dinh Tudn, 10T, THPT chuy0n LC Quf D6n; Gia Lai: Ttl Dirc Long,
i I Todn, THPT chuydn Hing Vuong; Cdn Tho: Vd Qu6'c Bd Cdn,12Al, THPT chuyen L! Tu Trong.
DANG HUNG THANG
*nii Tgl348. Xitc dinh s;i nghiam thtrc phdn bi€t niim trong khoang (O; Zr) ctio phwtng trinh
,:cos2'(8si16x*l2sina.r +lOsinr x)= e+1 (1)
1TPflT} P99 Yfl.Tq?I TTq, 23 TPflT} P99 Yfl.Tq?I TTq, 23 352 (10-2006) $', L,) it b, t D4r Br =Z i=l .$ I - ./-J , i=t Di lt. 8,,= o ta cd bi f+=tl,r, -8,-,) it bi i=1 D; t