When I can't your thanks, I check my answer again,my god......

50 more years ago,my dear teacher told me,if you solve a qustion with a pen,you only get 70,if you solve Q only with open eye,you get 80,...close eye, you get 100,...

I follow my teacher's a long time. ,...but,this time I lost ,...my answer is right only for a>1,

for a<1,this time, I only want to get 70.

You're  right at begaining,...but...

Q)A1=a,A2=a^a,...An=a^A(n-1)...,find limit(AN).

a=1,OK,ASR is 1, 0<a<1, AN is increase and has band 1,so it has limit, let it is x,From limit An=limit a^(n-1),we have x=a^x by continouity,this is a index function,we only can get answer by approximant....(a,x)=(.1,.399)=(.2,.469)=(.3,.529)=(.4,.585)=(.5,.641)=(.6,7)=(.8,.83)=(.9,.908).

If a>1 it is divergent,we can't use limit.

I'm very sorry for some "blind answers".