thank you for the effort. This is the only

example I have ever known that when you try to find the limit of a sequence, it will give you a false solution even you follow the right steps.  lna=(lnx)/x will have two solution when a is in (1,e^(1/e)).  The bigger one is not the solution.  Another example is (10^.1)^(10^.1)...

If we solve for x=(10^.1)^x, 10 is one of the solution.  But 10 is not the limit of the sequence.  The right limit is about 1.2.