To Jinjing-I found your solution

What is (2^0.5)^(2^0.5)^(2^0.5)...?

Your answer is

x^x^x^x^....if convergent, We have x=x^x , Lnx=xLnx, we get x=1,If x>1,It would be Divergent.

But I think it is wrong.  From x^x^x... convergent, you cannot get x=x^x.  Let's say x=.5.  .5, .5^.5, .5^.5^.5,... is convergent because it is increase and smaller than 1^.5^.5..., which is 1.  But you cannot say .5=.5^.5.

Since your reason is wrong, I am not sure that x^x^x^x^....is Divergent when x>1.

所有跟帖： 

• I'm very glad for your paper,but I'm right & you are ... -jinjing- ♀ (527 bytes) () 01/16/2011 postreply 11:14:42

• 回複：I'm very glad for your paper,but I'm right & you are ... -yma16- ♂ (323 bytes) () 01/16/2011 postreply 11:56:42

• Yes,you're right. -jinjing- ♀ (316 bytes) () 01/16/2011 postreply 13:07:13

• some calculators do not compute ^ correctly. -yma16- ♂ (378 bytes) () 01/16/2011 postreply 17:39:10

• Hi,If you try a<1,It convergent very fast. -jinjing- ♀ (130 bytes) () 01/16/2011 postreply 20:43:03

• 回複：Yes,you're right. -yma16- ♂ (414 bytes) () 01/16/2011 postreply 18:30:27

• 回複：回複：Yes,you're right. -jinjing- ♀ (205 bytes) () 01/16/2011 postreply 21:05:36

• I have to say I disagree with you. -yma16- ♂ (933 bytes) () 01/17/2011 postreply 09:51:33

• Thanks,but you are...,Newton was not clear,...100 more years Cau -jinjing- ♀ (287 bytes) () 01/17/2011 postreply 11:12:12

• When I can't your thanks, I check my answer again,my god...... -jinjing- ♀ (846 bytes) () 01/18/2011 postreply 12:31:15

• 回複：When I can't your thanks, I check my answer again,my god..... -yma16- ♂ (548 bytes) () 01/18/2011 postreply 14:22:39

• My friend,you'r great,a>e^(1/e) An is divergent. Why?Because... -jinjing- ♀ (127 bytes) () 01/18/2011 postreply 17:57:16

• thank you for the effort. This is the only -yma16- ♂ (450 bytes) () 01/20/2011 postreply 18:27:29

• Thanks,you are right. A old want to say....why the big one is no -jinjing- ♀ (302 bytes) () 01/21/2011 postreply 10:53:30

• I also found another example that taking a limit -yma16- ♂ (373 bytes) () 01/21/2011 postreply 17:42:54