(x3+13x)8的展开式中常数项为．

Question

((x)/(3)+(1)/(3x))8的展开式中常数项为 ______．

Answer 1

((x)/(3)+(1)/(3x))8展开式的通项Tr+1＝((1)/(3))8−r

C

r 8

x8−(4r)/(3)
令8−(4r)/(3)＝0解得r=6
故展开式的常数项为((1)/(3))2

C

6 8

＝(28)/(9)
故答案为(28)/(9)