Question

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256

Answer 1

=8-（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）
设s=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）
2s=1+1/2+1/4+......................................+1/128
相减s=1-1/256=255/256
所以8-255/256=7+1/256

Answer 2

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=（1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)+(1-1/256)
=1*8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/64)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/32)+1/256
=8-(1/2+1/4+1/8+1/16+1/16)+1/256
=8-(1/2+1/4+1/8+1/8)+1/256
=8-(1/2+1/4+1/4)+1/256
=8-(1/2+1/2)+1/256
=8-1+1/256
=7+1/256
所以，结果为：
七又二百五十六分之一
希望你能看懂，你能明白， 望采纳，赞同

Answer 3

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=（1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)+(1-1/256)
=1*8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/64)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/32)+1/256
=8-(1/2+1/4+1/8+1/16+1/16)+1/256
=8-(1/2+1/4+1/8+1/8)+1/256
=8-(1/2+1/4+1/4)+1/256
=8-(1/2+1/2)+1/256
=8-1+1/256
=7+1/256
所以，结果为：
七又二百五十六分之一
希望你能看懂，你能明白， 望采纳，赞同

Answer 4

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=（1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)+(1-1/256)
=1*8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-1+1/256
=7+1/256
=7又1/256

Answer 5

= 8-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256...
奥数么..答案自己算吧~这是过程喔~