# How do you find the radius of convergence #Sigma x^n/3^n# from #n=[0,oo)#?

The series has radius on convergence

Writing the series as:

and the total is:

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The radius of convergence is

The series ratio test is what we employ.

In order for the series to converge, we must

Consequently,

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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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