算1/9+1/99+1/999+1/9999+1/99999=?

算1/9+1/99+1/999+1/9999+1/99999=?
算1/9+1/99+1/999+1/9999+1/99999=?

算1/9+1/99+1/999+1/9999+1/99999=?
1/9+1/99+1/999+1/9999+1/99999=0.111...+0.0111...+0.00111...+0.000111...+0.0000111...=0.123455.=0.1234+0.00005555...
=0.1234+0.00005555...=0.1234+5/90000
=1234/10000+1/18000=22212/180000+10/180000=22222/180000=11111/90000

原式=1-1/10+1-1/100+1-1/1000+1-1/10000+1-1/100000=5-11111/100000=4.88889

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