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1、高中数学竞赛训练题--全解全析Thehighschoolmathcontest一problemsolvingIt，stwodifferentpositiveNumbers,andthey，resatisfied,andallpossibleintegers,c,makeit.Itisknownthattheinequalityistrueforallpositiveintegers,themaximumvalueofpositiveintegers,andprovesyourconclusion.Setthemonotonic
2、allyincreasingnumbercolumn,andsatisfy,tofindthegeneralformulafor{}・(1)makesure:(2)Verification:Let'ssetthenumbercolumn,Q:(1)whatisthevalueofthiscolumnin2010?(2)inthissequence,whatisthesequeneenumberofthe2010valueof1.Therearetenballsinred,blackandwhite・Nowputthemalli
3、ntoa,btwobags,requireseachbagthreecolorsoftheball,andpartyaandpartybtwobagsofthreecolors,equaltotheproductofthecount・Howmanywaystoputit.Theknownsequeneesatisfies(),theprecedingandthefirst,and,Remember,atthetime,isthereanypositiveintegerthatyouhaveforanypositiveinteg
4、er?IfIexist,findthevalueofm;Ifnot,explainwhy.Inthemiddle,already,theareaisequalto6.Thelengthofthetrilateral(I);(II)issetP(includingboundary),PtothetrilateralAB,BC,AB,andovaluerange・Inthesequence,agivennon-zerointeger・(1)if,(2)proof:theremustbeaninfinitenumberoftwodi
5、fferentconstants・Weknowthattheellipse,at(0,1),isarightAngle,andthesidesAB,BC,andellipsearehandedinBandC.IfthemaximumvalueoftheABCareaofthetriangleisequaltothevalueofthis.Figure,ellipse:,thevertexoftheellipse・(I),ififandonlyifthepointsontheellipseintheovalvertex,obta
6、inthemaximumandminimumvalues,thevaluerangeof；(II)ifthepointontheellipsetothemaximumdistancebetweenthefocus,theminimumvaluefor,andfellowshipwithstraightline,twopoints(notellipticalorvertex),andmeet・Trytoresearch:afixedline?Ifyouhaveafixedpoint,askforafixedpointcoordi
7、nate・Ifitisonlyafixedpoint,pleaseexplainwhy.Asshowninthefourpyramid,thebaseisthesquareofthelengthoftheside,thesideisapositivetriangle,andisperpendiculartothebase・(1)thevolumeofthefourpyramid;(2)isthereapointontheside?Pleaseexplainwhy.(二15outof10)Theequation：・(1)ifth
8、eequationrepresentsthecircle,therangeoftherealnumber;(2)whentheequationrepresentsthecircle,ifthecircleandthelineareintersectingattwopoints
