5-1/10-11/100-111/1000-···-111111111/1000000000=

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5-1/10-11/100-111/1000-···-111111111/1000000000=

5-1/10-11/100-111/1000-···-111111111/1000000000=
5-1/10-11/100-111/1000-···-111111111/1000000000=

5-1/10-11/100-111/1000-···-111111111/1000000000=
5-1/10=4.9
5-1/10-11/100=4.79
5-1/10-11/100-111/1000=4.679
5-1/10-11/100-111/1000-1111/10000=4.5679
……
可见结果是有规律的,整数为4,小数位数与最后要减去的数的分子的数位相同,依次按照7、6、5……减小
所以:
5-1/10-11/100-111/1000-···-111111111/1000000000=4.012345679