# Does #a_n=n*{(3/n)^(1/n)} #converge? If so what is the limit?

Substituting this back in, we get

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Yes, the sequence (a_n = n \left(\frac{3}{n}\right)^{\frac{1}{n}}) converges. The limit of this sequence as (n) approaches infinity is (e^3), where (e) is the base of the natural logarithm.

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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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- How do you use the integral test to find whether the following series converges or diverges #sum( 1/(n*ln(n)^0.5) )#?

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