1993 USAMO Problems/Problem 5: Difference between revisions
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== Problem | == Problem 5== | ||
Let <math>a_0, a_1, a_2,\cdots</math> be a sequence of positive real numbers satisfying <math>a_{i-1}a_{i+1}\le a^2_i</math> | Let <math>a_0, a_1, a_2,\cdots</math> be a sequence of positive real numbers satisfying <math>a_{i-1}a_{i+1}\le a^2_i</math> | ||
be a sequence of positive real numbers satisfying 
for 
. (Such a sequence is said to be log concave.) Show that for
each 
,
.
