(X2+1/X)n的展开式中,常数项是15求n

问题描述:

(X2+1/X)n的展开式中,常数项是15求n

(X2+1/X)^n=C(n,0)x^2n+C(n,1)x^(2n-2))b^1+…+C(n,r)x^(2n-2r)(1/x)^r+…+C(n,n)(1/x)^n
常数项是C(n,r)
(2n-2r)=r,
n=3/2r,
n=6,r=4,
C(6,4)=6*5/2=15