设 S=1/2+2/4+3/8+4/16+...+8/256 (1)两边同乘以1/21/2S = 1/4+2/8+3/16+.+7/256 +8/512 (2)(1)-(2)(1/2)S=1/2+1/4+1/8+1/16+.+1/256-8/512(1/2)S=1-1/256-4/256=251/256S=251/128