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

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?

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Accumulation points for a sequence indicates towards all subsequential limits.

Whenever a sequence converge, it have only one accumulation point.

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

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