首页 > 留学知识库

问题: 设n>2时,数列Cn1,

解答:

kC(n,k) = (k*n!)/[k!(n-k)!] = [n*(n-1)!]/[(k-1)!(n-k)!]
    = nC(n-1,k-1)
∴数列之和 = n[C(n-1,0)-C(n-1,1)+...+(-1)^(n-1)C(n-1,n-1)]
      = n(1-1)^(n-1)
      = 0................................C

或特殊值法,n=2时,数列之和=C(2,1)-2C(2,2)=0