1-2/3-2/9-2/27-2/81-2/243-2/729=

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1-2/3-2/9-2/27-2/81-2/243-2/729=1-2/3-2/9-2/27-2/81-2/243-2/729=1-2/3-2/9-2/27-2/81-2/243-2/729=1-2/

1-2/3-2/9-2/27-2/81-2/243-2/729=
1-2/3-2/9-2/27-2/81-2/243-2/729=

1-2/3-2/9-2/27-2/81-2/243-2/729=
1-2/3-2/9-2/27-2/81-2/243-2/729
=1-2/3-2/9-2/27-2/81-2/243-2/729-1/729+1/729
=1-2/3-2/9-2/27-2/81-2/243-3/729+1/729
=1-2/3-2/9-2/27-2/81-2/243-1/243+1/729
=1-2/3-2/9-2/27-2/81-1/81+1/729
=1-2/3-2/9-2/27-1/27+1/729
=1-2/3-2/9-1/9+1/729
=1-2/3-1/3+1/729
=1-1+1/729
=1/729

1-486/729-162/729-54/729-18/729-6/729-2/729可得到:
1-(486/729+162/729+54/729+18/729+6/729+2/729)=1-728/729=1/729