ConsidersequenceA1=a,An+1=a^Anfora>0.Ifthelimitxexists,wecantakethelimitonbothsidesandwillgetx=a^x,whichislna=ln(x)/x.Foraisin(0,1),thelimitisthesolutionoflna=ln(x)/x,whichislessthan1.
ln(x)/xis0atx=1andx->infinity.Themaxvalueoccursate^(1/e).
Whenaisin(1,e^(1/e)),
lna=ln(x)/xhastwosolutions.Weneedtousetheonethatislessthane^(1/e)asthelimit.
Anexampleisa=2^.5.(1)Anisincrease.(2)An&l...[阅读全文]
