document.write( "Question 1042128: How do I prove that: log5 4• log7 6•log9 8•...log81 80>1/2 \n" ); document.write( "

Algebra.Com's Answer #658496 by LinnW(1048) $\"\"$ $\"About$

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Suppose we convert each item to LN
\n" ); document.write( "So log5(4) = $\"ln%284%29%2Fln%285%29\"$ , log6(5) = $\"ln%285%29%2Fln%286%29\"$
\n" ); document.write( "and so forth
\n" ); document.write( "Our sequence will be
\n" ); document.write( " $\"ln%284%29%2Fln%285%29%2Aln%285%29%2Fln%286%29%2Aln%286%29%2Fln%287%29...\"$
\n" ); document.write( "Notice for the first 3 factors, we have $\"ln%284%29%2Fln%287%29\"$
\n" ); document.write( "and for the first 4 factors $\"ln%284%29%2Fln%288%29\"$
\n" ); document.write( "Notice the value in the denominator get larger as
\n" ); document.write( "we add factors. The numerator value remains fixed
\n" ); document.write( "while the denominator continues to increase.
\n" ); document.write( "So it appears that the we have convergence to 0 .
\n" ); document.write( " \n" ); document.write( "

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