# How do you use the Alternating Series Test?

Let us apply the test to the alternating series below.

Let us check the two conditions.

Hence, we conclude that the alternating series converges.

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To use the Alternating Series Test:

- Determine if the series is alternating, meaning the terms alternate in sign (positive, negative, positive, etc.).
- Check if the absolute value of the terms decreases as n increases.
- Verify that the limit of the absolute value of the terms as n approaches infinity is zero.
- If these conditions are met, then the series converges according to the Alternating Series Test.

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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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