SOLUTION: How do I prove that: log5 4• log7 6•log9 8•...log81 80>1/2

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Question 1042128: How do I prove that: log5 4• log7 6•log9 8•...log81 80>1/2
Found 2 solutions by LinnW, ikleyn:
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose we convert each item to LN
So log5(4) = ln%284%29%2Fln%285%29, log6(5) = ln%285%29%2Fln%286%29
and so forth
Our sequence will be
ln%284%29%2Fln%285%29%2Aln%285%29%2Fln%286%29%2Aln%286%29%2Fln%287%29...
Notice for the first 3 factors, we have ln%284%29%2Fln%287%29
and for the first 4 factors ln%284%29%2Fln%288%29
Notice the value in the denominator get larger as
we add factors. The numerator value remains fixed
while the denominator continues to increase.
So it appears that the we have convergence to 0 .

Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is not so simple.

There is an error in the proof.