# How to choose the Bn for limit comparison test?

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If the An is #(e^(1/n))/n#

how would you determine what bn to use to compare with this?

If the An is

how would you determine what bn to use to compare with this?

Note that

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To choose ( B_n ) for the limit comparison test, follow these steps:

- Select a series ( \sum a_n ) that you suspect behaves similarly to the series ( \sum b_n ).
- Choose ( B_n ) such that ( 0 < B_n < a_n ) for all ( n ) beyond some point.
- Compute the limit ( \lim_{n \to \infty} \frac{a_n}{B_n} ).
- If the limit is a positive finite number, then ( \sum a_n ) and ( \sum B_n ) either both converge or both diverge.
- If the limit is zero or infinity, consider choosing a different ( B_n ) and repeat the process until the limit meets the conditions outlined in step 4.

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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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