What does it mean if the interval of convergence of a series is #(-1,1)#?

Answer 1

A power series' interval of convergence is the range of x values at which the series converges.

In our case the series conevrges for x belonging to #(-1,1)#
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Answer 2

If the interval of convergence of a series is (-1,1), it means that the series converges for all values of x within the open interval (-1,1), but it diverges for x = -1 and x = 1.

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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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