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在 \({\left( {\frac{2}{x} - {x^2}} \right)^6}\) 的展开式中,常数项为( )
A.\(-60\)
B.60
C.\(-240\)
D.240
参考答案:D
解析:
由题知,展开式中第\(r+1\)项 \({T_{r + 1}} = {\rm{C}}_6^r{(\frac{2}{x})^{6 - r}}{( - {x^2})^r} = {( - 1)^r}{2^{6 - r}}{\rm{C}}_6^r{x^{3r - 6}}\),
令 \(3r - 6 = 0\),得 \(r = 2\),所以展开式中常数项为 \({T_3} = {2^4}{\rm{C}}_6^2 = 240\).
故选:D
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