What is (2^0.5)^(2^0.5)^(2^0.5)...?
Here is a solution.
Let it be x, then we get x=(2^0.5)^x. It seems it will lead x=2 or 4.
The limit should be unique. What is wrong with this method?
(Someone said that if x^x^x... (x>0) has a finite limit, x should
be <=e^(1/e). If he was right, then the maximum limit of x^x^x...
is e. So 4 cannot be the answer and 2 is. Is there a way to get
the answer directly (which is 2) and not use the maximum limit e to
reject 4?
)
May be you have seen it. Thanks anyway.
所有跟帖:
• It should be x=x^0.5.x^2=x,x=1,x=0 not good. x=(2^0.5)^x is not -jinjing- ♀ (121 bytes) () 10/26/2010 postreply 08:11:13