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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.

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It was done in class. Here it is, again:

0<2^{n}/n^{n} = 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.