# How do you solve the series (7 - 9 + (81/7) - (729/49) + ... )?

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7 - 9 + (81/7) - (729/49) + ...

How would you determine whether this is convergent or divergent? I'm not really sure where to even start. I think it's a geometric series? But I don't know how to get the formula for it...

7 - 9 + (81/7) - (729/49) + ...

How would you determine whether this is convergent or divergent? I'm not really sure where to even start. I think it's a geometric series? But I don't know how to get the formula for it...

This series is divergent

If you try out the first few terms, you will find that the sum/difference keeps getting further and further away from each other, approaching nothing.

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Diverges.

Write as an actual series first.

We see pretty clear patterns for the third and fourth terms, but the first and second terms are outliers, there is no obvious pattern.

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The series is divergent.

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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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