1/2+1/4+1/8+1/16+1/32+...+1/256简便运算
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![1/2+1/4+1/8+1/16+1/32+...+1/256简便运算](/uploads/image/z/438188-68-8.jpg?t=1%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B1%2F32%2B...%2B1%2F256%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97)
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1/2+1/4+1/8+1/16+1/32+...+1/256简便运算
1/2+1/4+1/8+1/16+1/32+...+1/256简便运算
1/2+1/4+1/8+1/16+1/32+...+1/256简便运算
1/2+1/4+1/8+1/16+1/32+...+1/256
=1-1/256
=255/256
1/2+1/4+1/8+1/16+1/32+...+1/256
=1/2+1/4+1/8+1/16+1/32+...+(1/256+1/256)-1/256
=1/2+1/4+1/8+1/16+1/32+...+(1/128+1/128)-1/256
=1/2+1/2-1/256
=1-1/256
=255/256
过程如下
1/2+1/4+1/8+1/16+1/32+...+1/256
=1/2+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+····(1/128-1/256)
=1/2+1/2-1/256(中间的正负抵消)
=1-1/256
=255/256