Question 1042128
Suppose we convert each item to LN
So log5(4) = {{{ln(4)/ln(5)}}}, log6(5) = {{{ln(5)/ln(6)}}}
and so forth
Our sequence will be
{{{ln(4)/ln(5)*ln(5)/ln(6)*ln(6)/ln(7)...}}}
Notice for the first 3 factors, we have {{{ln(4)/ln(7)}}}
and for the first 4 factors {{{ln(4)/ln(8)}}}
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 .