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

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

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

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256-1/256
=1/2+1/4+1/8+1/16+1/32+{1/64+[1/128+(1/256+1/256)]}-1/256
=1/2+1/4+{1/8+[1/16+(1/32+1/32)]}-1/256
=1/2+1/4+1/4-1/256
=1-1/256255/256

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
另
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

我也不会，而且我也是正在做这道题哦

飞都没

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256-1/256
=1/2+1/4+1/8+1/16+1/32+{1/64+[1/128+(1/256+1/256)]}-1/256
=1/2+1/4+{1/8+[1/16+(1/32+1/32)]}-1/256
=1/2+1/4+1/4-1/256
=1-1/256255/256

原式=（1-1/2）+（1/2-1/4）+（1/4-1/8）+（1/8-1/16）+（1/16-1/32）……+（1/128-1/256）
=1-1/256
=255/256

[1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256]*256/256
=(128+64+32+16+8+4+2+1)/256
=255/256
===============================================
三楼的 4255274 高手！
1/2=1-1/2
1/4=1/2-1/4
...
1/256=1/128-1/256