哈尔滨师大附中度高三上学期期末考试数学试题（理科）(2)

31因为f(3)?2,所以a(3?)2??2?a?124

321?f(x)?(x?)??x2?3x?2?f(1)?0,f(2)?024 （2）令x?1?an?bn?1?0,x?2?2an?bn?2n?1?0,

n?1??an?1?2则? n?1??bn?2?2 （3）(an?1?an)2?(bn?1?bn)2?(2n?2?2n?1)2?(2n?2?2n?1)2?22n?3 ?rn?1?rn?22n?32,rn?2?rn?1?22n?52,?q?2,?Sn??rn2

?Sn??(r12?r22???rn2)??r12[1?q2?q4???q2(n?1)]Sn1?q2???q2(n?1)14????? ?lim2?lim??2(n?1)n??rn??13qn1?422．（1）an?1??an?(1??)[an? （2）an?3n?(?2)n （3）当n?2k时，

66an?1],????2???6?0,???3或2 1??1??证明1an?1?113?2k?1??2k?12k2kan3?23?232k314?2k?32k3?22k32k??2232k?242??2k31334k?24k?22k32k22732k732k792k72k2k ?2(3?62)?0(??()???1)2k21221242?6?2111444491当n?2k时,??????????k???a1a2an98198294?32k?当n?2k?1时,111111?????????a1a2ana1an?12