Question

若(2x-)ⁿ展開式中含項(xiàng)的系數(shù)與含項(xiàng)的系數(shù)之比為-5,則n等于

A.4                   B.6                    C.8                    D.10

Answer 1

答案:B 解析:法一：將四個(gè)選項(xiàng)一一代入,根據(jù)二項(xiàng)式定理求1x²,1x⁴系數(shù),驗(yàn)證可得B選項(xiàng)正確.

法二：T_r+1=(2x)^n-r()^r=(-1)^r2^n-rx^n-2r,令n-2r=-2,r=+1,可得1x²系數(shù);令n-2r=-4,r=+2,可得系數(shù)為.

因?yàn)閮上禂?shù)之比為-5，可得n=6，選B.