简便计算1/2+1/4+1/8+1/16+.+1/128+1/256
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简便计算1/2+1/4+1/8+1/16+.+1/128+1/256
![简便计算1/2+1/4+1/8+1/16+.+1/128+1/256](/uploads/image/z/6884440-16-0.jpg?t=%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%971%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B.%2B1%2F128%2B1%2F256)
S=1/2+1/4+1/8+1/16+.+1/128+1/256
2S=1+1/2+1/4+1/8+1/16+.+1/128
S=2S-S
=1-1/256
=255/256
再问: 看不懂,求解释
再答: S=1/2+1/4+1/8+1/16+......+1/128+1/256 2S=2(1/2+1/4+........+1/256) =2*1/2+2*1/4+.....+2*1/256 =1+1/2+........+1/128 S=2S-S =(1+1/2+......+1/128)-(1/2+1/4+....+1/128+1/256) =1+(1/2+......+1/128)-(1/2+1/4+.....+1/28)-1/256 =1+0-1/256 =1-1/256 =255/256
2S=1+1/2+1/4+1/8+1/16+.+1/128
S=2S-S
=1-1/256
=255/256
再问: 看不懂,求解释
再答: S=1/2+1/4+1/8+1/16+......+1/128+1/256 2S=2(1/2+1/4+........+1/256) =2*1/2+2*1/4+.....+2*1/256 =1+1/2+........+1/128 S=2S-S =(1+1/2+......+1/128)-(1/2+1/4+....+1/128+1/256) =1+(1/2+......+1/128)-(1/2+1/4+.....+1/28)-1/256 =1+0-1/256 =1-1/256 =255/256