1+1\2+3\4+7\8+15\16+31\32+63\64+127\128等于多少?急用!

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1+1\2+3\4+7\8+15\16+31\32+63\64+127\128等于多少?急用!
1+1\2+3\4+7\8+15\16+31\32+63\64+127\128等于多少?急用!

1+1\2+3\4+7\8+15\16+31\32+63\64+127\128等于多少?急用!
原式=1+(1-1\2)+(1-1\4)+(1-1\8)+(1-1\16)+(1-1\32)+(1-1\64)+(1-1\128)
=1×8-(1\2+1\4+……+1\128)
=8-(1\2+1\4+……+1\128+1\128-1\128)
=8-(1\2+1\4+……+1\64+1\64-1\128)
=……
=8-(1\2+1\2-1\128)
=8-(1-1\128)
=7+1\128
=7又128分之1