2014年上海市高中数学竞赛(新知杯)试卷

201462014()(20143308301030)I604748)1n6(n6)(7o)(~o)xcosOTyTsinO=1nD211n22S=(an){n}S2+n+1a=1n1S11+n1+1t2l=4722S2+n+1sl(n--1)2+1+121+11n1+4n22z[l2(1)]{2n)2127z2(1)1=2X(1)1+2z1nl----4an-----2(--1)1+2nSSSSS(2)33Slsla{n}S=SSS+1(7z2){)nTl2aSSS=sS+1(ss-)sSn_--1j}+21)2ABCDab(n6o)ABCDX3ABCD3z(11)(z)z2z+{1}2--11SnStj}224Sa(1)72SS12(2)nSnS320146ao4{z}z=z+#(n12)z+zz++zzt_______________________5log(z2+2x3)z2+2x166a1a2a214122014S^=a++a^k=122014SSS7S{1211)S7789000010000100019999919806908613(o2]440285(53)U(13)61511719808880609DEFABC1BAF=aAEAF=F1EFAE+AF=[(bsinl5COSq+9,36cs5sim)+(f+csim)][(+9(14)ABCA=75AC=bAB=cABC10(14)7z271kk()127()11(16)z3zlzmin{zy)uk13zLu{++(min{zy}ZVZzY)12(16)12aIJ}=12n1b224x2--4y22+6206cosl5)sin+(c+6sinl5)co](2+bcosl5)2+(---23c+bsinl5)2r'--------------------------------------------------------62+c2+bc(cosl5+sinl5)32bz+cz+2bccos453273C+otsm151_a2--arctanABC~62+f2+c3ABCF2=c2c62+c2+k)1410k(7z1)(7z2)44820146(n)(z1)(2)(n--k)(n--k--1)(n--k)(n--k--1)k(k--1)(n--k)(n--k)(k1)(k2)+()(n1)+(k)(7zk1)+k(k1)(k)(7z1)(2)()4P6P=k=lRl2k=ln--_ki1n-17(1)JP=i4117-zmin{zY}{111zmin{z}u-+i2i1i12+cZZzzztfZ+c=c)z+44101++NYjj){+cY+czqqzqjj2IY)(2)2+9914++(+)+2(+)zzzzz4+2=13z2y=1z1on++131612z2m(m)122mak--Ima^m+a^m1m2mm+n^2m(1)1nm(m+12m)aaaaaan2m2m1a2mt(0tm1)a+1a+2a22m161n=2m+1(m)122m+1+m2m+1(1)1n^m(m+22m+1)a+1{12m+1)8a+l1a+2a+3a2+1n+a+a+6t+2a+3a+t1m+1aaa21a{2m2m1}a(2m1)aa1'a(f+1+m)a{t+t+m+12m+1}aaaaF2m+1(+m)+1](mf)2aaaaaa2114a121a+=2m+121n=2m+121+2-1=2n1216()