B0 ciAo DUC vA DAo oe r.lo Ki rm cuiNs rHUC THT CHqN HQC SINH GIOI QUoC GIA THPT NAM 2016 M6n : TOAIY Thoi gian : 180 phrit (khong kA thd.t gian giao di) Ngdy thi thri nh6t : 06t01/2016 tAhr ilHrhlH BAi aiefi GiAi h9 phuong rrinh I a*-y+zz I I *' - ,, =3 -l (x,y, z e IR) -22 = _2zz o*, - 3y, - y =o Bni (5 diad a) cho ddy s6 (a,,) xircdinh boi n ao =rn(2n2+r)-rn(n2 +r+r), v6i =1,2, Chung minh chi c6 hiiu hpn s5 n cho {a, } < b) cho dfiy sti (b,) xirc dinh b,i b, =rn(zn'+r)+rn(nz+n minh tdn tpi v6 h4n sd , cho +l), v6i n=r,2,,.chr?ng a' 2016 {6,,}.+ Trong dd {x} ld ky higu phAn 16 cria s,5 rhuc ;r : {x} = *_[r] Bni $ diad cho tam gi6c ABC c6 B, ccti dlnh, A thayddi cho tam gi6cABC nhgn' Gqi D ld trung di6m cria BC vir E, F tuong ung ri hinh chi6u vu6ng g6c c1,aD lln AB, AC a) GPi tqi M o ld tdm cria tluong trdn ngopi ti6p tam giitc ABC nF cit eo vit BCtan tuqt vdl/' chung minh dulng trdn ngopi titip tam g iirc AMNdi qua mQt tti6m co ointr b) c6c ti6p tuy6n cta dulng trdn ngopi ti6p tam giitc AEF t4i E, Chring minh ZthuQc m6t dudng thing cd Ointr F citnhau tai r BAi g di1m) Nguoi ta rr6ng hai loai cAy kh6c tr€n mOt mi6ng tl6t hinh chfr nh0t kfch thudc mxn vu6ng lmoi o tr6ng mQr cdy) MQt c6ch tr6ng Ja, aon gui rit dn tuqng n6u nhu: i) Sti.luqng c6y rlugc *6ng cfia hai lopi c6y bing nhau; ii) Sd lugng ch6nh lQch cria hai lopi c6y trOn m6i rrang kh6ng nh6 hon mQt n&a sri cira hang d6 vi si5 luqn8 ch€nh lQch cria hai lopi ciy tr6n ,,6i Jot r.no"g hon mQr nria sti cria cQt d6 *i a) Hay chi mQt crich tr6ng c6y Lntugng l$i m = n=2016 b) chring minh n6u c6 mQt crich trdng cdy 6n tugrlg thi c6 m Thf sinh khong ductc su hlng tdi li€u vd ntdy tinh can tay Cdn bo coi thi khong gidi thich gi thAm yit nrl6u li bQi cria