简便计算 1/2+1/4+1/8+1/16+1/32+1/64+1/108+1/216

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简便计算 1/2+1/4+1/8+1/16+1/32+1/64+1/108+1/216

简便计算 1/2+1/4+1/8+1/16+1/32+1/64+1/108+1/216
简便计算 1/2+1/4+1/8+1/16+1/32+1/64+1/108+1/216

简便计算 1/2+1/4+1/8+1/16+1/32+1/64+1/108+1/216
=1/2+1/4+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)+(1/64-1/108)+(1/108-1/216)
=1/2+1/4+1/4-1/216
=1-1/216
=215/216

原式=(1-1/2) (1/2-1/4) (1/4-1/8) (1/8-1/16) (1/16一1/32) (1/32-1/64) (1/64-1/1O8) (1/1O8-1/216)=1-1/216=215/216 望采纳