(1+x)(1−x)6展开式中x2项系数为．

Question

(1+x)(1−√(x))6展开式中x²项系数为______．

Answer 1

由题意可得，展开式(1−√(x)) 6的通项Tr+1＝

C

r 6

(−√(x)) r=(−1)r

C

r 6

x(r)/(2)
令r=2可得，T₃=C₆²x
令r=4可得，T₅=C₆⁴x²
∴当n=6时，展开式中x²项系数为，(1)/(2)n(n−1)+

C

4 n

=30
故答案为：30