1-1\\4-1\\8-1\\16-1\\32-164怎么简便计算
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![1-1\\4-1\\8-1\\16-1\\32-164怎么简便计算](/uploads/image/z/3834024-24-4.jpg?t=1-1%5C%5C4-1%5C%5C8-1%5C%5C16-1%5C%5C32-164%E6%80%8E%E4%B9%88%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97)
1-1\\4-1\\8-1\\16-1\\32-164怎么简便计算
1-1\\4-1\\8-1\\16-1\\32-164怎么简便计算
1-1\\4-1\\8-1\\16-1\\32-164怎么简便计算
1-1/4-1/8-1/16-1/32-1/64
=1-1/4-(1/4-1/8)-(1/8-1/16)-(1/16-1/32)-(1/32-1/64)
=1-1/4-1/4+1/8-1/8+1/16-1/16+1/32-1/32+1/64
=1-1/4-1/4+1/64
=33/64
因为
1/2+1/4+1/8+1/16+1/32+1/64=1-1/64
1-1/4-1/8-1/16-1/32-1/64=1-(1/4+1/8+1/16+1/32+1/64)
=1+1/2-(1/2+1/4+1/8+1/16+1/32+1/64)
=1+1/2-(1-1/64)
=1/2+1/64
=33/64
1-1\\4-1\\8-1\\16-1\\32-1/64
=1-(1/4+1/8+1/16+1/32+1/64+1/64-1/64)
=1-[1/4+1/8+1/16+1/32+(1/64+1/64)-1/64]
=1-[1/4+1/8+1/16+(1/32+1/32)-1/64]
=1-[1/4+1/8+(1/16+1/16)-1/64]
=1-[1/4+(1/8+1/8)-1/64]
=1-[1/4+1/4]+1/64
=1-1/2+1/64
=1/2+1/64
=33/64