(x/n+1)^n展开式中x^3的等于1/16 求n

题目

(x/n+1)^n展开式中x^3的等于1/16 求n

答案

(x/n +1)^n
coef.of x^3= 1/16
nC3.(1/n)^3 =1/16
[n(n-1)(n-2)/6](1/n^3) =1/16
8n(n-1)(n-2) =3n^3
8(n^2-3n+2) =3n^2
5n^2-24n+16=0
(5n-4)(n-4)=0
n=4