C(0,n)·1+C(1,n)·x+C(2,n)·x^2+...+C(n,n)·x^n = (1+x)^n同题目中两边积分，得C(0,n)·1/2+1/2C(1,n)·(1/2)^2+1/3C(2,n)·(1/2)^3+...+1/(n+1)C(n,n)(1/2)^(n+1)=1/(n+1)·((3/2)^(n+1)-1)
