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Summing Ones (Posted on 2013-02-27) Difficulty: 3 of 5
Find the sum
1+11+111+.......+111..111(n digits)

No Solution Yet Submitted by Danish Ahmed Khan    
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re: No Subject (spoiler) | Comment 3 of 4 |
(In reply to No Subject by Ady TZIDON)

If

sn=1/81*(10^(1+n)-9n-1)
 
then, when n=3, for example,
 
sn = (10^4 - 27 - 1) / 81 = 123.111111111111...
 
The formula could be changed to either:
 
sn=[1/81*(10^(1+n)-9n-1)]
 
where the square brackets indicate the floor function, or
 
sn=1/81*(10^(1+n)-9n-1) - 1/9
 
as the excess over an integer is always 1/9.

  Posted by Charlie on 2013-02-27 13:27:15
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