April 1st, 2014, 12:23 PM  #1 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Subsequence
2000 Real numbers are written on a row. Prove that it is possible to choose a subsequence such that the sum of the sum of the numbers of that subsequence differs maximum 1/1000th of a real number. (n1/1000 <= sum <= n+1/1000)

April 1st, 2014, 06:45 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra 
I presume you mean "1/1000th of a natural number".

April 1st, 2014, 09:22 PM  #3 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 
Yes indeed, sorry.


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