2010 AIME I Problems/Problem 14
Problem
For each positive integer n, let . Find the largest value of n for which
.
Note: is the greatest integer less than or equal to
.
Solution
Observe that is strictly increasing in
. We realize that we need
terms to add up to around
, so we need some sequence of
s,
s, and then
s.
It follows that . Manually checking shows that
and
. Thus, our answer is
.
See also
2010 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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