若(2x?1x)n展开式中含1x2项的系数与含1x4项的系数之比为-5,则n等于(  )A.4B.6C.8D.1

2025-06-28 22:50:12
推荐回答(1个)
回答1:

(2x?

1
x
)n展开式的通项为
Tr+1
C
(2x)n?r(?
1
x
)
r
=(-1)r2n-rCnrxn-2r
令n-2r=-2得r=
n+2
2

故含
1
x2
的系数为(?1)
n+2
2
2
n?2
2
C

令n-2r=-4得r=
n+4
2

故含
1
x4
项的系数为(?1)
n+4
2
2
n?4
2
C

(?1)
n+2
2
2
n?2
2
C
(?1)
n+4
2
2
n?4
2
C
=?5

将n=4,6,8,10代入检验得n=6
故选B