小学数学五年级的，要写算试。
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添项法，给最后加上 1/256 ，再减去1/256，可得2/256=1/128...
原式
= (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+2/256) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/64+1/128+ 1/128) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/64+2/128) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/64+ 1/64) - 1/256
= (1/2+1/4+1/8+1/16+1/32+2/64) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/32) - 1/256
= (1/2+1/4+1/8+1/16+2/32) - 1/256
。。。
= (1/2+1/2) - 1/256
=1 - 1/256
= 255/256
原式
= (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+2/256) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/64+1/128+ 1/128) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/64+2/128) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/64+ 1/64) - 1/256
= (1/2+1/4+1/8+1/16+1/32+2/64) - 1/256
= (1/2+1/4+1/8+1/16+1/32+1/32) - 1/256
= (1/2+1/4+1/8+1/16+2/32) - 1/256
。。。
= (1/2+1/2) - 1/256
=1 - 1/256
= 255/256
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1／2+1／4+1／8+1／16+1／32+1／64+1／128+1／256
=2／4+1／4+1／8+1／16+1／32+1／64+1／128+1／256
=3／4+1／8+1／16+1／32+1／64+1／128+1／256
=6／8+1／8+1／16+1／32+1／64+1／128+1／256
=7／8+1／16+1／32+1／64+1／128+1／256
=14／16+1／16+1／32+1／64+1／128+1／256
=15／16+1／32+1／64+1／128+1／256
=31／32+1／64+1／128+1／256
=63／64+1／128+1／256
=127／128+1／256
=255／256
=2／4+1／4+1／8+1／16+1／32+1／64+1／128+1／256
=3／4+1／8+1／16+1／32+1／64+1／128+1／256
=6／8+1／8+1／16+1／32+1／64+1／128+1／256
=7／8+1／16+1／32+1／64+1／128+1／256
=14／16+1／16+1／32+1／64+1／128+1／256
=15／16+1／32+1／64+1／128+1／256
=31／32+1／64+1／128+1／256
=63／64+1／128+1／256
=127／128+1／256
=255／256
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看不清啊，亲
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