The question is:
Determine whether the sequence a(n) = 2^n/n^n converges and then find its limit.
I think I know how to show that it converges using the fact that (2/n)^n needs to decrease, ie n>2.
But I have no idea how to find its limit. I don't know how to treat things of the x^x nature.
It was done in class. Here it is, again:
0<2n/nn = 2.2.2.....2/n.n.....n =(2/n)(2/n)...(2/n)<2/n
Use the squeeze theorem and apply the limit to the extremities of the above inequality.