1996 USAMO Problems/Problem 1
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Problem:
Prove that the average of the numbers is
.
Solution:
First, as we omit that term. Now, we multiply by
to get, after using product to sum,
.
This simplifies to
. Since
this simplifies to
. We multiplied by
in the beginning, so we must divide by it now, and thus the sum is just
, so the average is
, as desired.
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