用两种方法计算1/2+1/4+1/8+1/16+1/32+1/64

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用两种方法计算1/2+1/4+1/8+1/16+1/32+1/64

用两种方法计算1/2+1/4+1/8+1/16+1/32+1/64
用两种方法计算1/2+1/4+1/8+1/16+1/32+1/64

用两种方法计算1/2+1/4+1/8+1/16+1/32+1/64
1、原式=32/64+16/64+8/64+4/64+2/64+1/64=63/64
2、原式=1/2+1/4+1/8+1/16+1/32+(1/64+1/64)-1/64
=1/2+1/4+1/8+1/16+(1/32+1/32)-1/64
=1/2+1/4+1/8+(1/16+1/16)-1/64
=1/2+1/4+(1/8+1/8)-1/64
=1/2+(1/4+1/4)-1/64
=(1/2+1/2)-1/64
=1-1/64
=63/64