(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128,简便计算,

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(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128,简便计算,
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(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128,简便计算,
(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128,简便计算,

(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128,简便计算,
(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128
=(1/3)(1+1/2+1/4+1/8+1/16+1/32+1/64+1/128)*128
=(1/3)(1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/128)*128
=(1/3)(1+1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/128)*128
=(1/3)(1+1/2+1/4+1/8+1/16+1/16-1/128)*128
=(1/3)(1+1/2+1/4+1/8+1/8-1/128)*128
=(1/3)(1+1/2+1/4+1/4-1/128)*128
=(1/3)(1+1/2+1/2-1/128)*128
=(1/3)(1+1-1/128)*128
=(1/3)(2-1/128)*128
=(1/3)(255/128)*128
=255/3

(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384)*128
=(1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384+1/384-1/384)*128
=(2/3-1/384)*128
=((256-1)/384)*128
=255/3

原式=(128/384+64/384+32/384+16/384+8/384+4/384+2/384+1/384)
=(128+64+32+16+8+4+2+1)/3
=255/3
=85