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0.1+0.11+0.111+…+0.1111111111=.

题目详情
0.1+0.11+0.111+…+0.1111111111=______.
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答案和解析
0.1+0.11+0.111+…+0.1111111111,
=0.1+(0.1+0.01)+(0.1+0.01+0.001)+…+(0.1+0.01+…+0.0000000001),
=0.1×10+0.01×9+0.001×8+…+0.0000000001×1,
=1+0.09+0.008+0.0007+…+0.0000000001,
=1.0987654321;
故答案为:1.0987654321.