# How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma (-1)^(n+1)/sqrtn# from #[1,oo)#?

To determine if:

we can use use Leibniz' test, which states that a sufficient condition for an alternating series:

so the both conditions are met and the series is convergent.

and

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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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