2005 AIME II Problems/Problem 11
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Problem
Let be a positive integer, and let
be a sequence of reals such that
and
for
Find
Solution 1
For , we have
.
Thus the product is a monovariant: it decreases by 3 each time
increases by 1. For
we have
, so when
,
will be zero for the first time, which implies that
, our answer.
Solution 2
Plugging in to the given relation, we get
. Inspecting the value of
for small values of
, we see that
. Setting the RHS of this equation equal to
, we find that
must be
.
~ anellipticcurveoverq
Video solution
https://www.youtube.com/watch?v=JfxNr7lv7iQ
See also
2005 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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