(x2+1/x)6的展开式中X3的系数为

(x2+1/x)6的展开式中X3的系数为
(x2+1/x)6的展开式中X3的系数为

(x2+1/x)6的展开式中X3的系数为
(a+b)2 = a2+2ab+b2
(a+b)3 = a3+3a2b+3ab2+b3
(a+b)4 = a4+4a3b+6a2b2+4ab3+b4
观察系数1,4,6,4,1,其实就是C(4,0), c(4,1), c(4,2), c(4,3), c(4,4)
(a+b)6 = a6+6a5b+15a4b2+20a3b3+15a2b4+6ab5+b6
观察系数1,6,15,20,15,6,1,其实就是c(6,0), c(6,1), c(6,2), c(6,3), c(6,4), c(6,5), c(6,6,)
所以(x2+1/x)的展开式里各项分别为 x12, 6x9, 15x6, 20x3, 15, 6/x, 1/(x2)
x3的系数就是20

二项式定理
C6 3=20