1?t2?2t?02?bn单调减，∴3t?6mt??b1 ∴3t?6mt?0 ∴?2 ∴t?2或t??2
t?2t?03?2?x2?x?x19. (1)f'(x)?2axe?axe?xea(2?x)?0
?x?0 x?2
a?0 (??,0) 0 （0,2） 2 (2,??)
? ? ? ?
a?0 (??,0) 0 （0,2） 2 (2,??)
? ? ? ? ? (2)
<1>设切点（x0,y0）
??x01xea(2?x)?0?0e?x??x?1??y0?0 ??0
a?1e??2ax?y0?x0?e0?<2>令t(x)?f(x)?h(x)
x21t(x)?x?x?
xet'(x)?2xe?x?x2e?x?1?t?x??2xe?x?x2e?x?1?x(2?x)1?1? exx21 x21 2xt'(x)??x?2时t'(x)?0
(x?2?x)?1 ?0?x?2时x(2?x)?20?x(2?x)?1 ex2?t'(x)?0 ?t'(x)?0 ?t(x)在[0,??)b? ?t(1)?143?0 t(2)?2??0
2ee?x0?(1,2)使t(x)?0
?12x??cx(0?x?x0??x?g(x)?? 2x2??cx(x?x0)x??e?g(x)在上↑ （0，??）?11??2cx(0?x?x0)?2?x?g'(x)?? 22x?x??2cx(x?x0)x?e?2x?x2?2cx?0恒成立 xe?2c?2?x恒成立 ex2?x xex?3?0 ex令m(x)??m'(x)?x?3
?m(x)?m(3)
min2c??1 e3c??1 32e当c?0时
g'(x)?1??g(x)?
综上：c??1?2cx?0 x21 32e20.an?2?an?2∴{an}奇数项为AP d?2 （1）an?2??nn(n为奇)?2an （an）偶数项为GP q?2 ?an??
2??2(n为偶)kkk（2）b2k?1?b2k?a2k?1a2k?a2ka2k?1?(2k?1)?2?2(2k?1)?4k?2
S2n?(b1?b2)?(b3?b4)???(b2n?1?b2n)
?S2n?4[1?2?2?22?3?23??n?2n]
2S2n?4[1?22?2?23???(n?1)2n?n?2n?1] ??S2n?4[2?22???2n?n?2n?1]
S2n2(1?2n)??4[?n?2n?1]?(n?1)2n?3?8
1?2nn(3)Cn?(3n?1)2?(?1)
n??Cn??(2n?1)?2n?1(n为奇)
?(2n?1)?2?1(n为偶)111??(n?3) n为奇 Cn(2n?1)2n?12n?1111??(n?2) n为偶 nn?1Cn(2?1)2?1211[1?()n?1]1111152?????1?3?4???n?4?1?8?
1C1Cn42221?2
