=(ci +c|.2x2 +cf,.4x4 +...+CI.26 x''){x+t).
H0 sd cria xt trong khai triiin ld: C|.2=I2(lh6am6n y6u cAu bdi to6n). m6n y6u cAu bdi to6n).
o V6i n:2tac6: P(x) =(z*' +r)u (r*r)'
=(c! +c).zx' +Q.4xo +...+cf.26 x"){x' +zx+t).HQ s6 cria x' trong khai tritin ld: C1.2.2= 24 (kh6ng HQ s6 cria x' trong khai tritin ld: C1.2.2= 24 (kh6ng
th6a mdn ydu cAu bdi to6n).
o V6i n>3tac6: P(x) =(z*'*t)u (x+1)"
=(c! + ci.zx' + c!.4x0 + ...+ cf .zu x")
"(c! +c)x+Clx2 +Clx3 +...+Cix').
H0 sii cira x' trong khai tri6n l* C!.C3, + C).2.C).
Theo bdi ra ta c6: c[.c) + ci.z.c: =12 n(n -t\(, -z) e --1-l--- + l2n = 12 o(n-t)("' -Zn+lz)=0 <+ n = 1 (loai vi kh6ng th6a mdtn> 3).
rtit lufln: gi6 tn, n cAn tim ld n : I .
NhQn xet C6c b4n tham gia bdi ndy <t6u ph6t hiQn ttung
sai lim. C6c ban sau dua ra loi gi6i ngin ggn:
Hlr Giang: Nguydn Binh Duong, I I To6n, THPT chuy6n Hd Giang. Hung YOn: Chu Minh Huy,ll Todn
1, THPT chuy6n Hrmg Y6n; Dmrng HOng Scrn,
Nguydn Vi€t D[rc, TriQu Ninh Ngdn, 11,4.9, THPT
Ducrng Quing Him, VIn Giang. Hh finh: Nguydn
Quang Hitng, 70A1, THPT Cir Huy C4n. Vinh Long:
Chdu Minh Khdnh,l0Tl, THPT chuyCn Nguy6n Binh Khi6m. Tiiin Giang: LA Hodng Bdo, l0 To6n, THPT
. ^ -.1
chuyen Iren urang.
KIHTVI
%
@* *
1:0?
rong gid hgc Todn, sau khi hgc xong bdi Gi6i hqn a)a ddy s6, mQt hgc sinh ph6t bir5u, khing dinh ring minh c6 thil chimg minh dugc I : 0. Dugc
ThAy gi6o mdi l6n b6ng, b4n d6 hinh bdy chimg minh <16 nhu sau:
Ta c6: 1= liml =lim!
n
+ liml = o.
n
VQy I :0.
Thdy gitio khdng illnh cdch ch*ng minh trOn ld
sai. Bgn hdy chi ra chi sai giirp bgn iili nh6l l0 rrm rHONG
(GV THPT LC Qudng Chi, TX. K) Anh, Hd ITnh)
-. (r I I l)
=ltml -+-+-+...+- |
(r n n n)
=fim1+um1+tm1+...
nnn
^9 xu.{r nAN rtlDe+
sd 47',| (9.2016)
Tia so?n : 1 87B, phd Gieng [0, Ha Nqi 0T Bi6n EP:04.35121607
0r - tax Phat henh, Ifi su:04.35121606
Email: l0anh0Glu0ilreuielnam@gmail'c0m l*p thi I0[]l H9( ur IU0l nI
ffiuthemutic und Youth fflugurinennt't c5 viN xnon ngc nnt't c5 viN xnon ngc
cs. rsrn. NcuvEu cANH ToAN GS.TSKH.rnANvaNNrnxc
rs.NcuvrNvANvo5c
cs. ooaNQrrir.rtPGs.rs. rnANvANu.q.o PGs.rs. rnANvANu.q.o
:HIU rnAcn t'tntilu xuAr nAN
Chri tich HOi d6ng Thhnh vi6n
NXB Gi6o duc Vi€t Nam MACVAN]HIEN
Tdng Gi6m ddc NXB Gi6o duc Vi€t Nam GS.TS.WVANHTING
nrO tdng Gi6m ddc kicm Tdng biOn tQP
NXB Gi6o duc Vi0t Nam Ts. PHAN xuAN THANH
ruQt o6xc nruw rne
Tdns bian 4p : TS.rnAN frf,t] NLwt Thu ki Tda soan : Ths. n6 quaNc vrrvH zs. rnANr oNs cnAu, rls. NcuyEN eNu ofnrc, rs. rnA.N NRM otD.lc, rs. NcuvEN rrlrNs ol]c, rs. NcuveN MINH HA,
;.';*6fr6}{--r,-'14,,';;.;.-;"4;6; nAN, rrs. PHAM vAN uirNc, r'cs. rs. vo TITANH rruflr,
;;. #;. *o"*i ,o*-r"il"o* *or*., *roc rn*, rs. rHAM rHI BACH NGoc, pcs. rs. NcuvEN oANc psAr,pcs. rs. T4 DUy pHtxllrc, rm. NclirtN rrt6 rru.cs, GS.TSKH.DANG ImNG meNc, PGs. 7s. PIIAN DOAN troru' rns vu pcs. rs. T4 DUy pHtxllrc, rm. NclirtN rrt6 rru.cs, GS.TSKH.DANG ImNG meNc, PGs. 7s. PIIAN DOAN troru' rns vu
rrrra rstv, PGS.rS. vo otJONc rHUY, GS. rSra. Nco vGr rnuNc.
TRONG SO NAY
@ ciai bai ki trddc
Solutions to Preuious Problems
@ oii5" dAn d4y hgc To6n
Nguydn TiAn Tidn - MOt c6ch phAn tich
bidu thitc d&ng cdp bAc hai hai bidn vd itng dqng.
Trd.n Quang Hing - Ph6p ddi xilng tructrong thrrc hdnh giAi to6n. (Tidp theo kj trong thrrc hdnh giAi to6n. (Tidp theo kj
tni6c)
Problems in This Issue
TU47 I ..., TI.2/ 47 l, LLI 47 l, L2147 l. @ oanfr cho Trung hgc Co s&
For Lower Secondary School
Vfi. Hilu Chin - Ung dung v6'tinh chdt cria diy ti s6'bing nhau. (Tidp theo k1) tru6c)
@ Ciai d6p ddvui ngiy hd 1oqt 1)
(O oA thi vdo I6p 10 THPT chuy6n TP. He NOi,
nim hoc 201.6 - 2017.
l6p 10 Tnrdng THPT chuy6n DHSP He
N6i, n[m hoc 2016 -2077.
@ HrrAng d6n giii D6' thi tuydn sinh vio @ oi6" din phtt'ong ph6p giii todn
@ Cfrrdn b! cho k, thi THPT Qudc gia
Pham Trong Tht - GiAi Bdt phrrong trinh
v6 ti b[ng nhtng phrrong ph6p th6ng dqng.
@ ^, thi Olympic To6n hoc Qudc td (IMO) lAn
thr1 57 nim 2016
@ ffr,f sitc trddc ki thi - Dd sd I @ fiarrgAnh qua c6c bAi to6n - Bd.i s6'L2
Bii dich sd S - TiSng Anh qua c6c bdi to6n
@ ,a ra ki niy
@ s"i lAm 6 dau?
Giii dd,p: Sai 6 dAu?
LAThdTh1rug:7=0?
tc a-- .t/. w D T o N. !
&ir** }t{ilI uuultu tutlttu ti
C6c d6ng chi lSnh dAo voi gi6o vi,On ii6u bi6u trong
tC fy nigm 45 ndm ngdy B6c H6 grlri thu cho ngdnh gi6o duc
Vinh danh hgc sinh tr[ng tuy6n Dai hqc
trong Dai hQi Khuy6n hqc lAn thLp lV nhiQm ky 2015 - 2O2O
Ban chSp hdnh D6ng bo nhir truong nhiQm ky 2012-2015
Anh hirng phi cong Pham Nggc Lan vOi ThAy, trd nhd truong trong bu6i toa ddm nhdn chung lich srl voi th6 hO tr6 Duong Qudng Hirm
Vdn nghQ chdo mirng Li6n hoan Anh ngir Duong Qudng Hdm lAn thrl I - ndm 2015
J. ir' ThS. Nguy6n Van Thi6u
Bi thu d6ng iy, HiQu trudng nhd kudng
,QtrvottQ THPT Duong Qudng Hdm, Tinh Hung Yen toa b6n td ngan
t(1
| Sung Hong, tiep grdp voi th0 do Ha Noi, noi phat tich m6i tinh duyOn
\llmorng cci Chu Dong Tu -Ti6n Dung. DAy lii manh ddt co truydn thdng vdn hidn lAu doi, noi sinh ra nhidu anh hirng hdo kiet, danh nhAn van hoa lon crla dAn tOc. Truong duoc thdnh lAp ngdy 271912001. TrAi qua 15 ndm xAy dUng va phdt tridn truong da gat hai du-o.c nhidu thdnh tich ddng khich 10, dac bi6t duoc Chrl tich nuoc tang Huan chuong lao dQng h4ng lll nim 201 1 va trd
thdrnh dia chi gi6o duc ddng tin cAy c0a qu6 huong Xrl Nhdn.
Tru0c y6u cdu ddi moi cdLn bdn vd todrn di6n gido duc ddo t4o, Truong THPT
Dwng Qudng Hdm phdn ddu ddn ndn 2020 trd thdnh don vi hAng dAu vd chdt
lwng gido dr,tc ving ChAu thd Sdng Hdng, dia chi rdn duc, tuyQn tdi, ung vi€n cec tuong DAi hQc, co sd dAy ngh) trong nuoc vA Qucic t6 bdng cec phuong
tiQn hiQu qud, ddc biOt td ngoai ng? vd tin hQc, dAp ing hAi nhQp Qudc t6.Huang
theo su m6nh, muc ti6u do, Ban gidm hi6u luon quan tem tdi vioc giao duc toan di6n cho hoc sinh, tridn khai k6 hoach xay dung truong didn hinh ddi moi day hoc ngoai ng0 theo dd 6n NNQG 2020, day hoc theo dinh huong phdt lridn ndng lqc nguoi hoc vA gi6o duc kT ning s6ng,
Trong ching duong 15 nem qua, nhir trudng thudng xuy6n dugc UBND Tinh, 56 GiAo duc vd Oao tao quan tAm, dAm bAo cAc di6u kien tdt nhdt phuc vu hoat dQng dqy vd hoc. O6n nay 100% c6c phong hoc, phdng b0 mOn, phong ban chuc ndng d6u duoc trang bi mdy chi6u, mdy vi tinh, . . . ddp ring vi6c ung dung cong nghQ th6ng iin vdo hoat dOng day hqc. Dgi ngO cAn bQ, gido vi6n, hoc sinh
nhdr truong kh0ng ngung phdt tridn vd sd lugng, chdt lugng nen nhung nam qua nha truong da thu hoach duo.c nh0ng thdnh quA dAng ghi nhAn: Truong co 66 cAn b0 gi6o vi6n, trong d6 2i3 dat danh hi6u gido vi6n dqy gi6i cdc cdp, hon 1/4 gido vien co trinh dO tr6n chudn; d6i tuydn hoc sinh gi6i cdp tinh luOn dAn dAu
khdi cAc trudng THPT khong chuy6n; nhidu nem co hoc sinh d6 tht khoa dai hoc; nhd truong liOn tidp duo, c B0 Gido duc vd Ddo tao x6p trong tdp 200 truong THPT co didm thi dai hoc cao nhdt cd nuoc. Nim 2010 nha truong duoc c6ng nhAn truong dat chudn Qudc gia. B6n canh thdnh tich cao v6 chdt lugng gi6o dqc, nhd truong con chI trong c6c hoqt dQng trdi nghidm sdng tao, gieo duc kT
ndng sdng, td chfc cho hoc sinh giao luu v6i cAc truong THPT trong vd ngoai
Cdc dEi bi6u vd tQp th6 su pham nhd truong trong bu6i L5
c6ng b6 quyet Olnh b6 nhiQm hi6u trudng nhiQm ky 2013-2018
tinh, vdi nhAn chung lich s[r (Gido su Le Thi - co gAi k6o co trong ngdy Qudc khdnh 2/9/1945; anh hung Pham Ngoc Lan - chi6n si khOng quan dAu ti6n bdn ha mdy bay Mi tren bAu troi Ham Rdng, Thanh Hoa), tham h6i cac ba me ViCt
Nam anh hung, chdm soc nghia trang li6t si va di tich lich srj vdn hoa, . . . ThUc hi6n ch0 chuong xd hQi h6a gi6o duc cria Ddng vd Nha nuoc, ngdy 30 theng 4 nam 2002 HQi khuydn hoc Duong Qudng Hdm duoc thanh l4p do Anh
hing lao dQng, nhd gido NhAn dAn, GiAo su Duong Trong Bdi lam ch0 tich danh du. Cung voi Ban dai diQn cha me hoc sinh, HQi khuydn hoc Duong QuAng Hdrm
dd ddng hdnh trong sudt que trinh xay dLrng vd phat tridn cria nhd truong. Tu khi thanh lAp ddn nay, HQi dd huy dQng duoc cdc td chuc, c6 nhAn irng hQ tinh thdn,
vit chdt tri gi6 1 ,866 tj, ddng dd nha trudng tang cuong co sO val chdt, vinh danh khen thuong thAy gi6i, trd gi6i, cdp hac bdng cho hoc sinh gia dinh chlnh s6ch vdr
hoc sinh vuot kho vuon l6n trong hoc tAp, Hoi khuydn hoc Duong QuAng Hdm da
duQc TW HQi khuy6n hoc Vi6t Nam, UBND Tinh vd Hoi khuydn hoc Tinh Hung
YOn t4ng nhidu bang khen vd girdy khen vd thanh tich hoat dOng khuy6n hgc.
Nim hoc 2015-2016 ld ndm dien ra nhi6u su kiOn, cdc ngdy 16 lon cia dan toc,. thdy vd tro truong Duong Qudng Hdrm da phAt dQng cdc phong trdo thi dua vd gat hai duqc nhidu thdnh tich dn tuong: 16 dd tai nghidn cfu khoa hoc cria giao vi6n duoc xdp loai cdp ngdnh; 5/9 dQi tuydn hoc sinh gi6i cdc mOn vdn hoa duo. c x6p Nhdt ddng dQi cdp Tinh; 63 hoc sinh dqt giai trong cec ki thi chon hoc sinh gi6i cdp tinh, 1 t hoc sinh dat gidi hoc sinh gidi Qudc gia, tdng 16 giAi so voi ndm
hAc 201 4-201 5.
Dat duo, c nh0ng thdrnh tich dang tU hdo do, phdn lon nho sU quan tam, h6 tro cria cdc cdp I6nh dao, c6c ban ngdnh, cdc td chrrc dodn thd, ddc biet ld su n6 luc phdn ddu khOng ngung cira ldnh dao, gido vi6n, hoc sinh nhA trr.rong. Voi ch4ng duong 1 5 xdy dLng vdr phdt tridn, truong THPT Duong Qu6ng Hdm dd giu tron nidm tin c0a nhAn dAn, phu huynh vd cdc cdp lanh d4o. Huong tor ki niQm
15 nam ngdry thdnh l4p truong (2719/2001 - 271512016\ thdy vd tro nhd truongtidp tqc ddy manh hoc t4p vd kim theo tu tuong, d4o dth, phong cdch Hd Chl tidp tqc ddy manh hoc t4p vd kim theo tu tuong, d4o dth, phong cdch Hd Chl Minh, ra srh thi dua d4y tdt, hoc t6t, chinh phuc nh0ng dinh cao tri thrc moi, gop phdn ddi mor cdn bdn vd todn di6n giao duc ddro tao, d6p [ng cong nghi6p hoa, hien dai h6a dr{t nuoc.