Question

如果(2x2-

1

3 x

)n的展開式中含有非零常數(shù)項(xiàng)，則正整數(shù)n的最小值為______．

Answer 1

(2x2-

1

3 x

)n展開式的通項(xiàng)為Tr+1=

C

rn

(2x2)n-r(-

1

3 x

)r=(-1)r2n-r

C

rn

x2n-

7r

3

∵展開式中含有非零常數(shù)項(xiàng)
∴2n-

7r

2

=0即4n=7r有解
∵n∈N，r∈N
∴n是7的倍數(shù)
∴正整數(shù)n的最小值為7．
故答案為7