# Accumulation Values of a sequence

$$a_n=(1+ \frac{1}{n})^ {-4+n}$$

How do you find all the accumulation points of a sequence? I normally firstly look of the first members of the sequence and try to find a subsequences. Then calculate their limit and then I have the accumulation points.

I know that the sequence is increasing and that the limit of $$a_n= e$$. But I could not get further. Could you give me any tips for the problem and in general, how you proceed? And maybe is a stupid question, but if you have the limit of sequence is it so that the subsequences have the same limit as the limit of the sequence?

As your example,the only accumulation value is $$e$$