How do you know when a geometric series converges?

Answer 1
A geometric series #sum_{n=0}^inftyar^n# converges to #a/{1-r}# if #|r|<1#.
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Answer 2

A geometric series converges when the absolute value of the common ratio (r) is less than 1. In other words, if |r| < 1, the geometric series converges. If |r| ≥ 1, the series diverges.

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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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