问题 选择题
已知A=-
1998•1999
2000•2001
,B=-
1998•2000
1999•2001
,C=-
1998•2001
1999•2000
,则有(  )
A.A>B>CB.C>B>AC.B>A>CD.B>C>A
答案

设A=

n(n+1)
(n+2)(n+3)
,B=
n(n+2)
(n+1)(n+3)
,C=
n(n+3)
(n+1)(n+2)

则A=

n2+n
n2+5n+6
,B=
n2+2n
n2+4n+3
,C=
n2+3n
n2+3n+2

再由n2+5n+6>n2+4n+3>n2+3n+2;n2+n<n2+2n<n2+3n

可得:-C>-B>-A,

则C<B<A

故选A.

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