设s=1/2+1/2^2+1/2^3+...+1/2^n 则 2s=1+1/2+1/2^2+1/2^3+...+1/2^(n-1)则 2s-s=[1+1/2+1/2^2+1/2^3+...+1/2^(n-1)]-(1/2+1/2^2+1/2^3+...+1/2^n)得 s=1-1/2^n=(2^n-1)/2^n