# How do you use the limit comparison test for #sum 1 / (n + sqrt(n))# for n=1 to #n=oo#?

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To use the limit comparison test for the series (\sum_{n=1}^{\infty} \frac{1}{n + \sqrt{n}}), we need to compare it with a known series whose convergence behavior is established. We can choose to compare it with the harmonic series, (\sum_{n=1}^{\infty} \frac{1}{n}), since it is a commonly known series. By taking the limit as (n) approaches infinity of the ratio of the terms of the given series and the terms of the harmonic series, we can determine if the given series converges or diverges. If the limit is a positive finite number, then both series behave similarly, and if it's zero or infinity, then the behavior of the series differs.

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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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