# How do you find the positive values of p for which #Sigma n/(1+n^2)^p# from #[2,oo)# converges?

The series:

is convergent for

Consider the series:

Using this series for the limit comparison test:

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The series (\sum_{n=2}^{\infty} \frac{n}{(1+n^2)^p}) converges if (p > \frac{1}{2}).

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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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