如果(x+x乘根号x)^n的展开式中所有奇数项的系数和等于512,则展开式的中间项是什么?
人气:177 ℃ 时间:2020-07-02 21:26:13
解答
展开式中奇数项系数和就是奇数项的二项式系数和,即2^(n-1)=512,解得n=10.
展开式一共11项,中间项是第6项
T6=C(10,5)(x)^5*(x√x)^5=252*x^(25/2)
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