1-1/2-1/4-1/81……1/128-1/256=?注：一定要简便!

1-1/2-1/4-1/81……1/128-1/256=?注：一定要简便!
1-1/2-1/4-1/81……1/128-1/256=?注：一定要简便!

1-1/2-1/4-1/81……1/128-1/256=?注：一定要简便!
1-1/2-1/4-1/8……1/128-1/256
=1-(1/2+1/4+1/8+……1/128+1/256)
=1-(1/2+1/4+1/8+……1/128+1/256+1/256)+1/256
=1-(1/2+1/4+1/8+……1/128+1/128)+1/256
=1-(1/2+1/4+1/8+……1/64)+1/256
=……
=1-(1/2+1/2)+1/256
=1-1+1/256
=1/256

依题意得
原式=1-1/2-1/4-1/8-1/16-1/32-…-1/256
=1/2-(1/2-1/4)-(1/4-1/8)-(1/8-1/16)-(1/16-1/32)-...(1/128-1/256)
=1/2-1/2+1/4-1/4+1/8-1/8+1/16-1/16+1/32-...-1/128+1/256=1/256
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