How do you know When to use the nth term test for divergence on an infinite series?

Answer 1

Always apply this test.

This is the first test which one must apply when testing for the convergence/divergence of any series. The test is to see whether the nth term of the given series equal to 0 or not when n#->oo#. If it does not, then series would diverge.
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Answer 2

You use the nth term test for divergence on an infinite series when you're asked to determine if the series diverges or converges. Apply the nth term test by evaluating the limit as n approaches infinity of the nth term of the series. If this limit doesn't equal zero, the series diverges. If it equals zero or the limit doesn't exist, the test is inconclusive, and other tests may be needed.

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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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