(x-1/x^6)^2009的二项展开式中常数项为A.C(286,2009) B.C(287,2009) C.-C(286,2009)D.-C(287,2009)

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(x-1/x^6)^2009的二项展开式中常数项为A.C(286,2009) B.C(287,2009) C.-C(286,2009)D.-C(287,2009)
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(x-1/x^6)^2009的二项展开式中常数项为A.C(286,2009) B.C(287,2009) C.-C(286,2009)D.-C(287,2009)
(x-1/x^6)^2009的二项展开式中常数项为
A.C(286,2009) B.C(287,2009) C.-C(286,2009)D.-C(287,2009)

(x-1/x^6)^2009的二项展开式中常数项为A.C(286,2009) B.C(287,2009) C.-C(286,2009)D.-C(287,2009)
(x-1/x^6)^2009的二项展开式中常数项为
T‹k+1›=[C(2009,k)][x^(2009-k)][1/x^6]^k=[C(2009,k)]x^(2009-7k)
由2009-7k=0,得k=287,故常数项为C(2009,287),故应选B.