1/2+1/4+1/8...1/1024=
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1/2+1/4+1/8...1/1024=1/2+1/4+1/8...1/1024=1/2+1/4+1/8...1/1024=1/2+1/4+1/8...1/1024=1/2+1/4+1/8...1/
1/2+1/4+1/8...1/1024=
1/2+1/4+1/8...1/1024=
1/2+1/4+1/8...1/1024=
1/2+1/4+1/8...1/1024
=1/2+1/4+1/8...1/1024+1/1024-1/1024
=1/2+1/4+1/8...+1/512+1/512-1/1024
=……
=1/2+1/4+1/8+1/8-1/1024
=1/2+1/4+1/4-1/1024
=1/2+1/2-1/1024
=1-1/1024
=1023/1024
1/2+1/4+1/8...+1/1024
=1/2+1/4+1/8...+1/1024+1/1024-1/1024
=1-1/1024（注意这步是从1/1024+1/1024算起，注意你就找的到规律了）
=1023/1024