计算：1/2+1/4+1/8···+1/128+1/256=________.
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设a=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
2a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128 (上式乘2）
则
2a-a=a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 )
=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1-1/256
=255/256
2a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128 (上式乘2）
则
2a-a=a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 )
=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1-1/256
=255/256
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