2008 AIME II Problems/Problem 6
Revision as of 23:34, 4 July 2013 by Nathan wailes (talk | contribs)
Problem
The sequence is defined by
The sequence
is defined by
Find
.
Solution
Rearranging the definitions, we have
from which it follows that
and
. These recursions,
and
, respectively, correspond to the explicit functions
and
(after applying our initial conditions). It follows that
.
From this, we can determine that the sequence corresponds to the triangular numbers.
See also
2008 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.