perplexus.info :: Numbers : Summing Ones

Home > Numbers

Summing Ones (Posted on 2013-02-27)

Find the sum
1+11+111+.......+111..111(n digits)

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

re: No Subject (spoiler)

| Comment 3 of 4 |

(In reply to No Subject by Ady TZIDON)

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

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info