作业帮请问1/2+1/4+1/8+1/16.+1/256怎么简便算?谢谢!
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请问1/2+1/4+1/8+1/16.+1/256怎么简便算?谢谢!
请问1/2+1/4+1/8+1/16.+1/256怎么简便算?谢谢!
请问1/2+1/4+1/8+1/16.+1/256怎么简便算?谢谢!
1/2+1/4+1/8+1/16.+1/256
=（1-1/2）+（1/2-1/4)+(1/4-1/8)+(1/8-1/16).+(1/128-1/256)
=1-1/2+1/2-1/4++1/4-1/8+1/8-1/16+1/16-.-1/128+1/128-1/256
=1-1/256
=255/256
=8-(1-1\\256) =7又256分之255 2分之1+4分之3+8分之7+16分之15+32分之31+64分之63+128分之127+256分之255 =8-（1/2+1/4+1/8+
用公式计算
1/2+1/4+1/8+1/16.....+1/256
=[1/2-1/256*1/2](1-1/2)
=1-1/256
=255/256
望采纳~~~~~