>>12792755The first term is good near 1
Compute ln(3)/ln(2) = 1 + ln(3/2)/ln(2)
stopping here gives ~ 1+ ((1/2)/(5/2))/(1/3)) = 8/5 = 1.6
Continuing gives 1+ ln(3/2)(ln(3/2) + ln(4/3)) = 1+ 1/(1+ln(4/3)/ln(3/2))
stopping here gives ~ 1+1/[1+ ((1/3)/(7/3))/((1/2)/(5/2))] = 19/12 = 1.58333...
Continuing gives 1 + 1/(1 + ln(4/3)/(ln(4/3)+ln(9/8))) = 1+1/(1+1/(1+ln(9/8)/ln(4/3)))
stopping here gives ~ 1+1/(1+1/(1+((1/8)/(17/8))/((1/3)/(7/3)))) = 65/41 = 1.58536...
Continuing gives 1+1/(1+1/(1+ln(9/8)/(ln(9/8)+ln(32/27)))) = 1+1/(1+1/(1+1/(1+ln(32/27)/ln(9/8))))
stopping here gives ~ 1+1/(1+1/(1+1/(1+((5/27)/(59/27))/((1/8)/(17/8))))) = 550/347 = 1.58501...
