由于111…1n个1=19×999…9n

由于

111…1

n个1=
1
9×

999…9

n个=
10n-1
9                       
∴1+11+111+…+

111…1

n个1=
1
9[(10-1)+(102-1)+…+(10n-1)]
=
1
9(10+102+…+10n)-
n
9
=
1
9•
10(1-10n)
1-10-
n
9
=
10n+1-9n-10
81