(C0/n)²＋(C1/n)²+(C2/n)²＋…＋(Cn/n)²值证明等于C2/2n.急

(C0/n)²＋(C1/n)²+(C2/n)²＋…＋(Cn/n)²值证明等于C2/2n.急
(C0/n)²＋(C1/n)²+(C2/n)²＋…＋(Cn/n)²值证明等于C2/2n.急

(C0/n)²＋(C1/n)²+(C2/n)²＋…＋(Cn/n)²值证明等于C2/2n.急
(1+x)^n的展开式子中x^k的系数是C(n,k)
(1+x)^2n的展开式子中x^n的系数是C(2n,n)
(1+x)^2n=[(1+x)^n][(1+x)^n]=(求和C(n,k)x^k)*(求和C(n,j)x^j)
所以x^n的系数是[C(n,0)C(n,n)+C(n,1)C(n,n-1)+.+C(n,n)C(n,0)]
=[C(n,0)^2+C(n,1)^2+.+C(n,n)^2]