# How do you use the integral test to determine the convergence or divergence of #Sigma 1/n^(1/3)# from #[1,oo)#?

The sum

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To use the integral test to determine the convergence or divergence of the series Σ 1/n^(1/3) from n = 1 to infinity:

- Evaluate the integral ∫(1/x^(1/3)) dx from 1 to infinity.
- If the integral converges, then the series Σ 1/n^(1/3) also converges. If the integral diverges, then the series Σ 1/n^(1/3) also diverges.

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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 show that the series #ln1+ln2+ln3+...+lnn+...# diverges?
- How do you Find the limit of an infinite sequence?
- How do you know when to use the integral test for an infinite series?
- How do you know when to use the Ratio Test for convergence?

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