# How do you determine if #a_n = (1+1/n^2)^n# converge and find the limits when they exist?

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To determine the convergence of the sequence ( a_n = (1+\frac{1}{n^2})^n ), you can use the fact that ( e ) is the limit of ( (1+\frac{1}{n})^n ) as ( n ) approaches infinity. Therefore, ( a_n ) approaches ( e ) as ( n ) approaches infinity. Hence, the sequence converges to ( e ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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