如何简便计算111111111\9?

如何简便计算111111111\9?
如何简便计算111111111\9?

如何简便计算111111111\9?
=100000000/9+10000000/9+1000000/9+100000/9+10000/9+1000/9+100/9+10/9+1/9
=(99999999+1)/9+(9999999+1)/9+(999999+1)/9+(99999+1)/9+(9999+1)+(999+1)+(99+1)/9+(9+1)/9+1/9
=(11111111+1/9)+(1111111+1/9)+(111111+1/9)+(11111+1/9)+(1111+1/9)+(111+1/9)+(11+1/9)+(1+1/9)+1/9
=11111111+1111111+111111+11111+1111+111+11+1+(1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9)
=12345678+1
=12345679

可以把原数字拆分
原式=100000000/9+10000000/9+1000000/9+100000/9+10000/9+1000/9+100/9+10/9+1/9
=(99999999+1)/9+(9999999+1)/9+(999999+1)/9+(99999+1)/9+(9999+1)+(999+1)+(99+1)/9+(9+1)/9+1/9
=(1111111...

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可以把原数字拆分
原式=100000000/9+10000000/9+1000000/9+100000/9+10000/9+1000/9+100/9+10/9+1/9
=(99999999+1)/9+(9999999+1)/9+(999999+1)/9+(99999+1)/9+(9999+1)+(999+1)+(99+1)/9+(9+1)/9+1/9
=(11111111+1/9)+(1111111+1/9)+(111111+1/9)+(11111+1/9)+(1111+1/9)+(111+1/9)+(11+1/9)+(1+1/9)+1/9
=11111111+1111111+111111+11111+1111+111+11+1+(1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9)
=12345678+1
=12345679

收起

规律是
123456789*9=1111111101
12345679*9= 111111111
1234569*9= 11111121
123459*9= 1111131
12349*9= 111141
1239*9= 11151
129*9= 1161
19*9= 171
9*9= 81