1977 IMO Problems/Problem 2
Revision as of 16:42, 29 January 2021 by Hamstpan38825 (talk | contribs) (Created page with "==Problem== In a finite sequence of real numbers the sum of any seven successive terms is negative and the sum of any eleven successive terms is positive. Determine the maximu...")
Problem
In a finite sequence of real numbers the sum of any seven successive terms is negative and the sum of any eleven successive terms is positive. Determine the maximum number of terms in the sequence.
Solution
Let be the given sequence and let . The conditions from the hypothesis can be now written as and for all . We then have: a contradiction. Therefore, the sequence cannot have terms. In order to show that is the answer, just take 16 real numbers satisfying . We have and for . Thus we found all sequences with the given properties.
The above solution was posted and copyrighted by enescu. The original thread for this problem can be found here: [1]
See Also
1977 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |