令Sn=1/2+2/4+3/8+4/16+.+n/2^n,1/2Sn=1/4+2/8+3/16.+n/2^n+1,Sn-1/2Sn=1/2+1/4+1/8+.+1/2^n+n/(2^n+1),1/2Sn=-(1/2-1/2^n)+n/(2^n+1) Sn=-2((1/2-1/2^n)+n/(2^n+1))