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问题 选择题
已知(x2+
1
x
)n的二项展开式的各项系数和为32，则二项展开式中x4的系数为（　　）
A．5B．10C．20D．40
答案

在(x2+

1
x
)n中，令x=1得到二项展开式的各项系数和为2n

∴2n=32

∴n=5

∴(x2+

1
x
)n=(x2+
1
x
)5

其展开式的通项为Tr+1=C5rx10-3r

令10-3r=4得r=2

∴二项展开式中x4的系数为C52=10

故选B．

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