2007年高考数学四川文科(详细解答)

2即y?(xn?4)?2xn(x?xn)．

2令y?0，得?(xn?4)?2xn(xn?1?xn)． 2即xn?4?2xnxn?1．

显然xn?0，∴xn?1?xn2?． 2xnxn2xn2(xn?2)2(xn?2)2?，知xn?1?2???2?（Ⅱ）由xn?1?，同理xn?1?2?． 2xn2xn2xn2xn 故

xn?1?2x?22?(n)．

xn?1?2xn?2xn?1?2x?2?2lgn，即an?1?2an．所以，数列{an}成等比数列．

xn?1?2xn?2n?1从而lg故an?2a1?2n?1lgx1?2?2n?1lg3． x1?2即lgxn?2?2n?1lg3． xn?2n?1xn?2?32 xn?2从而

所以xn?2(32?1)32n?1n?1?12(3

2n?1n?1（Ⅲ）由（Ⅱ）知xn??1)32?1，

∴bn?xn?2?n?1432n?1?1?0

bn?132?11111∴?2n?2n?1?2n?1?21?1?

bn33?13?133当n?1时，显然T1?b1?2?3． 当n?1时，bn?111bn?1?()2bn?2?L?()n?1b1 333∴Tn?b1?b2?L?bn

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?b13?L?(11?b13)n?1b1

b[1?(1?1)n3] 1?13?3?3?(13)n?3．

综上，Tn?3(n?N*)． / 14

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