题目内容：

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256

优质解答

令m=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
两边同时乘2,得：
2m=1+1/2+1/4+1/8+...+1/128
两式相减,得：
m=1-1/256=255/256
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=（1-1/2)+(1/2-1/4)+(1/4-1/8)+...+(1/128-1/256)
=1-1/2+1/2-1/4+1/4-1/8+...+1/128-1/256
=1-1/256
=255/256