What is Nth Term Test for Divergence of an infinite series?

Answer 1

Nth Term Test (also called Divergence Test)

If #lim_{n to infty}|a_n| ne 0#, then #sum_{n=1}^inftya_n# diverges.
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Answer 2

The Nth Term Test for Divergence states that if the Nth term of an infinite series does not approach zero as n approaches infinity, then the series diverges. In other words, if lim(n→∞) an ≠ 0, then the series Σan diverges. However, if lim(n→∞) an = 0, it does not necessarily mean that the series converges; further tests are needed to determine convergence.

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Answer from HIX Tutor

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.

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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